Combine sugar, ½ teaspoon cinnamon, nutmeg, and allspice in a bowl.

Whip egg whites with an electric mixer on high speed until soft peaks form. Reduce speed to medium and beat, gradually adding ½ of sugar mixture, until stiff peaks form.

Beat egg yolks in a separate bowl until thick and lemon colored. Mix remaining sugar mixture into the yolks.

Fold yolk mixture into the egg whites. Add milk and half-and-half; combine gently.