Process beans and milk together in a blender until smooth; pour into a small saucepan.
Stir sugar, egg, orange zest, ginger, and cornstarch into the bean mixture until smooth; place over medium heat and cook, stirring constantly, until thickened, about 30 minutes.
Stir butter and vanilla extract into the thickened mixture until the butter is melted; pour into 4 dessert cups and refrigerate until chilled, at least 15 minutes.
