Preheat & Prep: Preheat oven to 350°F. Lightly grease a 9-inch tart pan with a removable bottom.
Make the crust: In a food processor, pulse all-purpose flour, almond flour, powdered sugar, and salt until combined. Add melted butter and vanilla. Pulse until the mixture looks like wet sand and holds together when squeezed. If too dry, add 1 tablespoon cold water.
Press the crust: Dump mixture into tart pan. Use fingers or flat measuring cup to press evenly across bottom and up sides. Prick bottom with a fork. (Don't press too hard – a light, even hand is better.)
Chill and blind bake: Freeze crust for 15 minutes (prevents shrinking). Bake directly on middle rack – no pie weights needed – for 18-22 minutes, until edges are golden and bottom looks dry and set. Let cool completely in pan on a wire rack. Do not skip this step.
Make the filling: While crust cools, whisk mascarpone, sugar, heavy cream, and vanilla bean paste until smooth. It should be thick but spreadable – like very soft cream cheese. If too stiff, whisk in another tablespoon of cream. Taste: it should be barely sweet, with mascarpone leading.
Assemble: Spread mascarpone mixture evenly into cooled crust. Use an offset spatula for a smooth top. Slice peaches thin (about 1/4-inch) and arrange in overlapping circles starting from outside edge working inward, overlapping each slice by half so no cream shows underneath. It should look like a flower.
Chill for texture: Refrigerate tart for at least 2 hours, ideally 4. This firms the mascarpone for clean slices. (In a rush? 45 minutes in the freezer works, but don't tell anyone.)
Optional glaze: Before serving, warm 1 tablespoon apricot jam with 1 teaspoon water and brush over peaches for a lacquered, professional look.