In the bowl of a stand mixer fitted with the paddle attachment, combine 2 cups (250 grams) flour, granulated sugar, yeast, salt, and cardamom. Add warm milks, and beat at low speed until combined. Add 1 egg (50 grams), and beat until combined. Gradually add remaining 1⅔ cups (208 grams) flour, beating just until dough comes together and stopping to scrape sides of bowl.

Switch to the dough hook attachment. With mixer on low speed, add butter, one cube at a time, beating until combined after each addition. Beat until dough is elastic and smooth, 8 to 10 minutes.

Spray a large bowl with cooking spray. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 2 to 2½ hours. (Alternatively, cover and refrigerate dough overnight. Let it come to room temperature and then let rise in a warm, draft-free place [75°F/24°C] until doubled in size, 2 to 2½ hours, before proceeding.)

Line 2 baking sheets with parchment paper. Spray 2 large sheets of plastic wrap with cooking spray.

Lightly punch down dough. Cover and let stand for 10 to 15 minutes. Turn out dough onto a lightly floured surface, and divide into 12 portions (about 74 grams each). Using the palm of your hands, gently shape each portion into a round, smooth ball, lightly flouring your hands as needed. Place 3 to 4 inches apart on prepared pans. Cover with plastic wrap, spray side down, and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 1½ to 2 hours.

Preheat oven to 375°F (190°C).

Place Coconut Pastry Cream in a pastry bag fitted with a medium round piping tip.

Using your fingers or a ¼-cup measuring cup, gently press an indentation into center of each bun. Pipe pastry cream into indentations. (Do not overfill; pastry cream will expand during baking.)

In a small bowl, whisk remaining 1 egg (50 grams) until well combined. Using a pastry brush, brush egg all over top and sides of dough, avoiding pastry cream.

Bake until golden brown and an instant-read thermometer inserted near center registers 190°F (88°C), 9 to 11 minutes. Let cool completely on pans on wire racks.

In another small bowl, whisk together confectioners’ sugar and 2 tablespoons (30 grams) room temperature water until well combined. Using a pastry brush, brush glaze on sides of buns, and immediately garnish with coconut flakes, if desired. Serve immediately. Refrigerate in airtight container for up to 3 days.

In a medium saucepan, heat milks and ¼ cup (50 grams) sugar over medium heat, whisking frequently, until steaming. (Do not boil.)

In a medium bowl, whisk together egg yolks, cornstarch, salt, and remaining ¼ cup (50 grams) sugar. Slowly add warm milk mixture, whisking constantly. Pour mixture into saucepan; cook over medium heat, whisking constantly, until thickened and boiling, 4 to 5 minutes. Whisk in extracts.

Strain mixture through a fine-mesh sieve into a large bowl. Whisk in butter until melted and well combined. Cover with a piece of plastic wrap, pressing wrap directly onto surface of pastry cream to prevent a skin from forming. Refrigerate until an instant-read thermometer registers 65°F (18°C) to 70°F (21°C), 2½ to 3 hours.