Scale the ingredients
Scale factor = desired yield ÷ original yield
For 750 ml from a 500 ml recipe, multiply ingredients by 1.5. Do not multiply simmering time by 1.5: evaporation depends on pan area and heat. Season near the end.
Roux: weigh the fat and flour
Equal weights of butter and flour make a practical starting roux. For 500 ml milk or light stock, use about 20 g each for a light sauce, 30 g each for medium body, or 40 g each for a thick filling. These are starting points for pale roux; darker roux thickens less.
To add body to an already-cooked sauce, cook a small extra roux separately, whisk some sauce into it until smooth, then combine and simmer until the flour taste is gone. Sprinkling raw flour straight into the pot mostly manufactures lumps.
Vinaigrette: the 3:1 starting point
For 120 ml dressing, begin with 90 ml oil and 30 ml acid. For 240 ml, use 180 ml oil and 60 ml acid. Taste on a leaf and adjust. Mustard helps the mixture stay together; it does not repeal gravity.
Reduction: specify what remains
Reduction % = (starting volume − final volume) ÷ starting volume × 100
Reducing 500 ml to 250 ml removes 50% of the volume. Reducing it to 125 ml removes 75%. “Reduce by half” and “reduce to half” happen to agree; most other fractions do not.
As a rough model, halving the volume doubles salt concentration. If the sauce is already salty enough, stop reducing. Thickening and concentrating are different jobs.
Small slurry, measured correction
For about 250 ml thin sauce, mix 1 tsp cornstarch with 1 tbsp cold water. Whisk in half, bring to a gentle boil for about a minute, and check before adding more. It changes texture and is not a substitute for gelatin-rich jus, but dinner does not require a purity tribunal.