Make pie dough: Pulse flour, salt, and sugar in a food processor. Add butter and pulse until mixture resembles coarse meal, with some larger pieces remaining. Drizzle ¼ cup water over mixture. Pulse until mixture just begins to hold together. If dough is too dry, add ¼ cup more water, 1 tablespoon at a time, and pulse (or mix with a fork).

Divide dough, wrap, form disks, and refrigerate: Divide dough in half onto two pieces of plastic wrap. Gather into two balls, wrap loosely in plastic, and press each into a disk using a rolling pin. Refrigerate until firm, well wrapped in plastic, 1 hour or up to 1 day.

Fit dough into pie plate: On a lightly floured surface, roll out 1 disk pâte brisée to a 13-inch round, about ⅛ inch thick. (Reserve remaining disk for another use.) Fit dough into a 9-inch pie dish and press into bottom edges and up the sides. Trim edge, leaving a 1-inch overhang; fold edge under and crimp as desired. Freeze 15 minutes.

Preheat oven; line pie plate with parcment and pie weights: Preheat the oven to 375°F with the rack located in the lower third. Line crust with parchment paper, gently pressing the parchment into the edges of the crust; weigh down parchment with dried beans or pie weights.

Bake crust: Bake until the edges of the pastry begin to turn golden, about 15 minutes. Carefully remove pie weights and parchment paper. Continue to bake until crust is golden brown in color, about 10 minutes more. Transfer the crust to a wire rack to cool slightly.

Make filling: Melt butter in a medium saucepan. Add flour and cook, whisking, over medium heat for 2 minutes (do not let flour darken). Whisk in milk, cream, sugar, and vanilla. Bring to a boil; reduce heat to medium-low and simmer until thickened, 5 to 7 minutes.

Strain filling into crust and bake: Strain mixture into cooled crust and bake until filling is slightly set, about 25 minutes. Let cool completely on a wire rack before serving.