Name: Horseradish Sauce
Ingredients: 2 tablespoons cold milk; 1 pint milk; 2 tablespoons flour; 2 tablespoons butter; 2 eggs; 1 tablespoon mustard; ¼ cup vinegar; Chili vinegar (optional); Finely chopped onion (optional)

Why it works: Mustard and onion match in chemistry and in kitchens. They rank in the top 6% of all ingredient pairs, and cooks put them together in 9,259 recipes. Both carry 2-isopropyl-3-methoxypyrazine, which smells earthy, pea. The science ↓

Horseradish Sauce

Ingredients

Directions

In a small bowl, mix 2 tablespoons of cold milk with 2 tablespoons of flour until smooth.
In a clean saucepan, heat the remaining milk until it simmers.
Pour in the flour and milk mixture and add the butter. Boil for 5 minutes, stirring constantly to prevent burning.
Remove from heat and let cool slightly. Stir in the well-whisked eggs, mustard, and vinegar.
Once completely cool, transfer to a bottle and seal tightly.

Recipe from a historical cookbook (Internet Archive).

Transcribed from a scanned cookbook and modernised for today's kitchens. Where the book gave no heat or time, or said "a moderate oven", the temperatures and times here may be modern equivalents rather than the book's own figures.

Explore the science

The flavor team

The pairs that carry this dish. Each one is judged two ways: how much their aromas overlap, and how often cooks already put them together.

Mustard + oniontop 6% of all pairs

Smell alikestrong

Cooked together9,259 recipes

Shared aroma: 2-isopropyl-3-methoxypyrazine (earthy, pea).
Milk + buttertop 7% of all pairs

Smell alikemoderate

Cooked together81,283 recipes

Shared aroma: (z)-4-heptenal (biscuit, cream).
Mustard + vinegartop 7% of all pairs

Smell alikemoderate

Cooked together14,067 recipes

Shared aroma: isobutyraldehyde (malty, green).
Flour + buttertop 12% of all pairs

Smell alikelow

Cooked together124,287 recipes

Shared aroma: isobutyraldehyde (malty, green).
Flour + mustardtop 13% of all pairs

Smell alikemoderate

Cooked together5,066 recipes

Shared aroma: isobutyraldehyde (malty, green).

Flour and butter barely smell alike, yet cooks put them together in 124,287 recipes: they work on texture and structure more than aroma.

Ranks compare each pair with 20,000 random ingredient pairs on CompKitchen. How we score pairs

Swap the onion

The recipe marks onion as optional. How well each one fits the dish's main ingredients (milk, flour, butter, egg, mustard, vinegar):

Shallotfits better
Chivefits better
Horseradishfits better
Onionthe original

Fit is the average pairing score against milk, flour, butter, egg, mustard, vinegar. Candidates are from the same food group and used in at least 100 recipes.