For crust: In the bowl of a stand mixer fitted with the paddle attachment, beat butter, confectioners’ sugar, and salt at medium speed until creamy, 1 to 2 minutes, stopping to scrape paddle and bottom and sides of bowl. Add egg yolk; beat until well combined. Beat in vanilla.
In a medium bowl, whisk together flours. With mixer on low speed, gradually add flour mixture to butter mixture, beating just until a dough forms and stopping to scrape sides of bowl.
Spray 9 (2¾x1-inch) round tart pans with baking spray with flour; place on a rimmed baking sheet.
Divide dough into 9 portions (about 31 grams each); roll each portion into a ball. Press a dough ball into bottom and up sides of each prepared tart pan; trim any excess dough. Freeze for 15 minutes.
Position oven rack in bottom third of oven. Preheat oven to 400°F (200°C).
For filling: In a small saucepan, whisk together cheeses, granulated sugar, milk, egg, cornstarch, and salt until smooth and well combined. Cook over medium heat, whisking constantly, until sugar dissolves and mixture is thickened and steaming. (Do not boil.) Remove from heat; whisk in butter and vanilla until butter is melted and mixture is smooth.
Strain mixture through a fine-mesh sieve into a medium liquid-measuring cup with a spout, discarding solids. Divide strained mixture among prepared crusts (about 2 tablespoons or 30 grams each).
In a small bowl, whisk together egg yolk and 1 tablespoon (15 grams) water; gently brush on top of filling.
Bake until crust and top of filling are lightly browned and an instant-read thermometer inserted in center registers 165°F (74°C) to 170°F (77°C), 10 to 13 minutes, rotating baking sheet halfway through baking. Let cool in pans for 15 minutes. Serve warm, or let cool completely on a wire rack. Best served same day as made. Refrigerate in an airtight container for up to 2 days.