Pour milk into a microwave-safe glass or ceramic bowl. Cook in the microwave on high until hot but not boiling, 2 to 4 minutes.

Combine sugar, flour, and salt in a second microwave-safe glass or ceramic bowl. Whisk in hot milk gradually until incorporated. Cook in the microwave on high in 1-minute intervals, stirring after each interval, until thickened, 4 to 5 minutes.

Whisk eggs in a medium bowl until pale and frothy. Whisk 1/3 cup milk mixture into eggs gradually, then whisk egg mixture into remaining milk mixture until smooth. Cook in the microwave on high until custard is thickened, about 2 minutes. Allow to cool slightly.

Stir vanilla into custard until incorporated. Cool completely in the refrigerator before using, about 30 minutes.