Do not pour eggs into hot milk; instead, add the hot milk to the eggs a little at a time. This is called tempering, and it gradually raises the eggs’ temperature. When eggs meet hot liquid all at once, they coagulate immediately and leave strands in the mixture. Whisk the eggs and sugar together without delay as well, because sugar left sitting on top of the yolks draws out moisture and creates a grainy texture.
The problem comes from how eggs react to heat. As egg proteins warm, they bond together and coagulate. When that bonding happens slowly and evenly, the mixture turns into a silky custard; when it happens suddenly, the egg clumps into solid pieces. An egg poured into boiling milk coagulates within seconds. That is why the two mixtures should not be combined directly; first bring their temperatures closer together. The same rule applies when tempering hot soup with egg, and the technique is used in many parts of cooking.
Use this order: whisk the egg yolks and sugar together in a bowl, adding starch at this stage if needed. With the bowl held steady on a towel, pour the hot milk into the eggs in a thin stream while whisking continuously. Start with about one ladleful; once the mixture has warmed, add the rest more quickly. Reversing the direction and pouring the eggs into the pot does not give the same result. Place a damp towel under the bowl to keep it from slipping and leave two hands free.
The order for adding sugar is also important and often overlooked. If sugar sits on top of the egg yolk, it draws out moisture and leaves small, hard grains on the surface. These grains will not dissolve later and will feel sandy in the custard. So, as soon as you add the sugar to the yolk, whisk it immediately. The mixture is ready when it becomes pale yellow and slightly fluffy. Sift in the starch at this stage too, because lumps of starch will not disperse later.
Return the combined mixture to the pot and cook over medium heat, continuously scraping the bottom. In recipes containing starch, bring the mixture to a boil; for thin custards without starch, do not boil it—remove it from the heat once it coats the back of a spoon. Choose a heavy-bottomed pot and keep the heat at medium. If the burner is turned to high, the mixture may scorch on the bottom and the burned flavor will spread through the custard. Once the mixture starts to thicken, whisk faster because it sets within seconds. The mixture may begin to splatter as it approaches a boil; wear an oven mitt at this point to protect against splashes.
If small lumps still form, the custard is not necessarily ruined. Pour it through a fine-mesh strainer to remove the curds and smooth it out; straining is good practice and is included at the end of many recipes. A badly curdled mixture may be partially rescued by briefly blending it. Cover the surface of the custard with plastic wrap, pressing it directly against the surface to prevent a skin from forming. Cooling the custard in a wide, shallow dish helps it cool quickly; refrigerate it within 2 hours of cooking.