Stir sugar, cornstarch, and salt together in a saucepan. Stream milk and half-and-half into the saucepan while stirring to dissolve the sugar mixture.
Bring the mixture to a boil, reduce heat to medium, and cook, stirring continually, for 2 minutes. Remove saucepan from heat; stir peanut butter and vanilla extract into the milk mixture until smooth.
Divide the mixture into 4 small serving dishes and refrigerate until firm, at least 30 minutes.
