On a lightly floured surface, roll Pâte Sucrée into a 12-inch circle (about ⅛-inch thickness). Carefully transfer to a 9-inch fluted round removable-bottom tart pan, lightly pressing into bottom and up sides. Using a paring knife, trim excess dough. Using a fork, dock bottom of dough. Refrigerate until firm, at least 30 minutes.
Preheat oven to 325°F (170°C).
Top dough with a piece of parchment paper, letting ends extend over edges of pan. Add pie weights.
Bake until edges are set, about 15 minutes. Carefully remove parchment and weights, and brush bottom of crust with egg white. Bake until surface of crust is dry and lightly browned, about 15 minutes more. Let cool completely in pan. Increase oven temperature to 350°F (180°C).
In the bowl of a stand mixer fitted with the paddle attachment, beat butter and granulated sugar at medium speed until light and creamy, 2 to 3 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition and stopping to scrape sides of bowl. Beat in vanilla, salt, and almond extract. With mixer on low speed, gradually add flours, beating until combined. Spoon frangipane into a pastry bag, and cut a ¼-inch opening in tip.
Spread preserves in an even layer on bottom of prepared crust. Pipe frangipane over preserves. Using a small off set spatula, smooth frangipane. Top with almonds.
Bake until frangipane is set and just golden, about 30 minutes. Let cool in pan for 20 minutes. Remove from pan, and let cool completely on a wire rack.
When ready to serve, in a small bowl, whisk together confectioners’ sugar and milk. Spoon into a pastry bag, and cut a ⅛-inch opening in tip; pipe glaze on top of tart as desired. Serve immediately, or let stand until glaze is set. Refrigerate in an airtight container for up to 3 days.