For dough: In a small bowl, stir together warm milk, yeast, and ¼ teaspoon (1 gram) sugar. Let stand until foamy, about10 minutes.

In the bowl of a stand mixer fitted with the paddle attachment, combine all-purpose flour, lemon zest, salt, and remaining 3 tablespoons (36 grams) sugar. Add yeast mixture and eggs, and beat at low speed until a shaggy dough forms; scrape sides of bowl.

Switch to the dough hook attachment. With mixer on low speed, add butter, 1 tablespoon (14 grams) at a time, beating until combined after each addition. Increase mixer speed to medium-low, and beat until dough is soft and elastic and does not stick to your hands when touched, 10 to 15 minutes.

Spray a large bowl with cooking spray. Place dough in bowl, turning to grease top. Cover and refrigerate overnight.

For filling: In the bowl of a stand mixer fitted with the paddle attachment, beat butter and sugar at medium speed until light and creamy, 2 to 3 minutes. Add egg yolks, one at a time, beating well after each addition and stopping to scrape sides of bowl. Beat in extracts.

In a small bowl, whisk together almond flour, all-purpose flour, and salt. With mixer on low speed, gradually add flour mixture to butter mixture, beating until combined.

Line 3 baking sheets with parchment paper.

Lightly punch down dough. Very lightly dust work surface with all-purpose flour; turn out dough onto prepared surface, and divide in half. Roll half of dough into a 13-inch square. (Wrap remaining dough in plastic wrap, and refrigerate.) Trim ½ inch off all sides to create a 12-inch square; cut dough into 9 (4-inch) squares. Place dough pieces on prepared pan. Repeat procedure with remaining dough.

Place 1 dough square so that one point is facing you. Using a pastry brush, brush edges of dough with beaten egg. Using a small offset spatula, spread 1 heaping tablespoon (15 grams) filling down center of dough (about 2 inches long). Place 2 apricot halves, cut side down, on filling. Pull and fold side points of dough to center of pastry; gently pinch dough points together and fold under, gently pressing to adhere. Return to pan. Repeat procedure with remaining dough pieces, remaining filling, and remaining apricot halves, placing 2 inches apart on pans. Cover with lightly greased plastic wrap, and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 45 minutes to 1 hour. (See Note.)

Preheat oven to 350°F (180°C).

Gently brush pastry with beaten egg; top with sliced almonds.

Bake, one pan at a time, until golden brown, about 20 minutes, rotating pan halfway through baking. Let cool on pans for 15 minutes. Brush warm preserves onto warm pastries. Serve warm, or let cool completely. Refrigerate in an airtight container for up to 3 days. Best served same day as baked.