Mayonnaise

Set a medium bowl on a damp folded towel so it cannot spin while you whisk one-handed. Add the egg yolk, mustard, vinegar, and salt and whisk for a full 30 seconds until the mixture is smooth, slightly paler, and slightly thickened. Everything must be at room temperature — a cold yolk emulsifies sluggishly and is far quicker to break. The mustard is not just flavor here: it is a second emulsifier that makes the sauce far more forgiving.

This is the whole game. Whisking constantly and hard, add the oil drop by drop for the first quarter of it — wait until each addition has fully disappeared before adding more. As the mixture thickens and lightens, you can relax to a thin, steady thread of oil, still whisking without pause. The base is grabbing oil droplets and locking them apart in a network; rush it and the network never forms. By the time the oil is in, you will have a thick, pale, jiggling mound.

Taste the emulsion — it will be flat and oily-rich and need brightening. Whisk in the lemon juice for acidity and lift, then adjust salt. If the mayonnaise is stiffer than you want, or looks dull and greasy, whisk in cold water a few drops at a time: it both loosens the sauce and re-tightens a slightly oily-looking emulsion, restoring the satin sheen. Chill at least an hour before serving; the flavors round out and it firms slightly.