Prepare Ube Pastry Cream: In a medium saucepan, combine the ube powder and milk over medium heat, whisking continuously until it thickens, about 5–7 minutes. Remove from heat, stir in sugar and butter until smooth, and refrigerate.

Make Coconut Dough: Cream together unsalted butter, brown sugar, and granulated sugar until light and fluffy. Add the eggs and coconut extract, then incorporate flour and shredded coconut until just combined.

Make Ube Dough: Blend butter and sugar until creamy, then add ube powder and eggs. Mix well before incorporating flour to form a sticky dough.

Assemble Cookies: Roll out coconut dough, place ube pastry cream in the center, cover with ube dough, and seal tightly.

Freeze Dough: Arrange cookies on a baking sheet and freeze for at least 2 hours.

Bake: Preheat oven to 350°F (175°C) and bake cookies for about 12 minutes until edges are set.

Cool & Top: Let cookies cool for 5 minutes before transferring to a wire rack. Melt chocolate and dip ube besito onto cookies.