+++
categories = ["food"]
date = 2025-02-22T11:51:00-06:00
description = ""
draft = false
slug = "hot-fudge"
title = "🍦 Hot Fudge"
author = "nicholas"
+++

I want to make the the [NYTimes Hot Fudge Sauce](https://cooking.nytimes.com/recipes/6094-hot-fudge-sauce) recipe. The recipe provides mostly volume measurements, so I will have to convert these to weight values. Also as usual, I will stubbornly substitute some ingredients for more shelf-stable and/or cheaper options.

## NYTimes Recipe
This is the list provided by the NYTimes recipe. Every single ingredient quantity except chocolate is provided by volume.

| quantity | ingredient                              |
| -------- | --------------------------------------- |
| 2 cups   | heavy cream                             |
| 4 tbsp   | unsalted butter                         |
| ½ cup    | light brown sugar                       |
| ¾ cup    | granulated sugar                        |
| ¼ tsp    | fine sea salt                           |
| 2 oz     | bittersweet chocolate (in small pieces) |
| 1¼ cups  | sifted high-fat Dutch-process cocoa     |
| ½ tsp    | vanilla extract                         |

## Substitutions
### heavy cream → (water + oil + dry milk powder)
The recipe requires 2 cups of heavy cream. The density of heavy cream is something like 1.01 to 1.03 g/mL, so 2 cups of heavy cream weighs approximately 484 grams. I will use this weight as the basis for calculating the amounts of each substitution ingredient. I simply multiply their respective proportions by the total weight. The table below is the resulting values:

**heavy cream nutrient breakdown**
| nutrient      | proportion | weight |
| ------------- | ---------- | ------ |
| water         | 0.58       | 281    |
| carbohydrates | 0.04       | 19     |
| protein       | 0.02       | 10     |
| milk fat      | 0.36       | 174    |

The water and fat substitutions are trivial: water is water, and milk fat is (as far as the substitution is concerned) fat, but I still need to account for 19 grams **carbohydrates** and 10 grams **protein**. Heavy cream is a dairy product, basically milk. So I will replace the carbs and protein that is missing as a result of its absence with non-fat milk powder. This product is basically heavy cream with the water and fat removed.

**non-fat milk powder nutrient breakdown**
| nutrient      | proportion | weight |
| ------------- | ---------- | ------ |
| carbohydrates | 0.52       | 15     |
| protein       | 0.35       | 10     |

Non-fat milk powder has approximately what I am missing: 15 grams of carbs and 10 grams of protein. Good enough.

**substitution breakdown**
| nutrient      | substitution         | weight |
| ------------- | -------------------- | ------ |
| water         | water                | 281    |
| carbohydrates | milk powder          | 29     |
| protein       | milk powder          |        |
| milk fat      | vegetable shortening | 174    |

### unsalted butter → (water + oil)
The recipe requires 4 tbsp. unsalted butter. This weighs 56 grams. Once again, however, I will substitute this relatively expensive ingredient with cheaper, more shelf stable ingredients: **oil** and **water**.

**unsalted butter nutrient breakdown**
| nutrient | proportion | weight |
| -------- | ---------- | ------ |
| milk fat | 0.80       | 45     |
| water    | 0.2        | 11     |

The substitution is 1:1:

**substitution breakdown**
| nutrient | substitution | weight |
| -------- | ------------ | ------ |
| milk fat | water        | 45     |
| water    | water        | 11     |


### fine sea salt → table salt
The recipe requires 1/4 tsp. fine sea salt. I will be substituting fine sea salt with table salt, which has a relative density of 0.90. According to the label on my table salt, ¼ tsp. weighs 1.5 grams. I will need 1.35 grams of table salt. 

### vanilla extract → imitation vanilla
They really nailed this substitution. Imitation is functionally identical to vanilla extract. I substitute it 1:1.

## Conversions
I do not document every conversion here. Nutrition labels typically provide volume *and* weight values for a serving size. It is not very interesting.

### Dutch-process cocoa
This one is tricky. The recipe requires 1 ¼ US cups high-fat Dutch-process cocoa, sifted _then_ measured. I have no interest in learning how they scoop and measure their volume of cocoa powder, so I will just defer to the numbers provided on the nutrition label and convert directly. According to this, 1 Tbsp. weighs 6 grams, and I need 1.25 cups.

*Tbsp in 1.25 cups*

$1.25 \times 16 = 20$

*grams of cocoa in 20 Tbsp.*

$20 \times 6 = 120$

**I will need 120 grams of Dutch process cocoa.**

### Vanilla Extract
 ½ tsp. vanilla extract has a density of close enough to 1.0 g/mL. 1 tsp. is 5 mL.

**I will need 2.5 grams of vanilla extract.**

## Result
This table is the result of the substitutions and conversions above.

| ingredient             | weight |
| ---------------------- | ------ |
| water                  | 292    |
| oil                    | 219    |
| nonfat dry milk powder | 29     |
| granulated sugar       | 144    |
| light brown sugar      | 96     |
| salt                   | 1.35   |
| bittersweet chocolate  | 57     |
| dark cocoa powder      | 120    |
| vanilla extract        | 2.5    |
| _TOTAL_                | _961_  |

### Process
Naturally I will rewrite the process to account for my substitutions:

1. In a saucepan, combine oil, sugars, water, and salt. Bring to a simmer over medium-low heat. Simmer 45 seconds. Add chocolate, and whisk to dissolve. Remove from heat, add cocoa, and whisk until no lumps remain.
2. Return pan to low heat, and simmer sauce until glossy, whisking constantly, 20 seconds. Remove from heat, and stir in vanilla. Serve warm. 

To reheat sauce, warm in a saucepan over low heat, stirring constantly. Do not boil.