Heat the Milk Mixture. Whisk together milk, vanilla extract, and sugar in a saucepan; heat until steaming (not boiling).
1 1/8 cups milk, 3/4 teaspoon vanilla extract, 5 tablespoons sugar
Prep the Yolks. In a separate bowl, whisk egg yolks, cornstarch, and 2 tablespoons of the lukewarm milk mixture until smooth.
3 egg yolks, 2 1/2 tablespoons cornstarch
Temper the Eggs. Slowly whisk a few spoonfuls of hot milk into the yolk mixture, repeating 3–4 times to prevent curdling.
Cook Until Thick. Pour everything back into the saucepan; cook over medium heat, stirring constantly, until thick and bubbling (2–4 minutes).
Remove and Whisk. Take off heat and whisk for about a minute to smooth out any lumps.
Stir in Peanut Butter. Add creamy peanut butter and stir until fully blended.
1/4 cup peanut butter
Taste and Adjust. Stir in salt, then taste and add more salt or sugar if needed.
1/8 teaspoon salt
Strain if Desired. For extra smoothness, press through a fine-mesh sieve.
Cover and Chill. Lay plastic wrap on the surface to prevent a skin; cool at room temperature. Refrigerate (covered) if making in advance.