Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper. Whisk the 3 tbsp cocoa powder, 3 tbsp granulated sugar, and 1 tbsp flour together in a small bowl, then stir in the 2 tbsp melted butter, 2 tbsp whole milk, and 1/2 tsp vanilla extract until you have a thick, smooth paste.

Unfold the 1 sheet of thawed puff pastry on a lightly floured surface and cut it into 4 even squares. Spoon a heaped tablespoon of filling onto one triangle half of each square, leaving a 1/2-inch border around the edges.

Beat the 1 egg with the 1 tbsp water. Brush the egg wash along the edges of each square, fold diagonally into a triangle, press to seal, and crimp firmly with a fork. Brush the tops with the remaining egg wash.

Place the turnovers on the prepared baking sheet, cut 2 small slits in the top of each, and bake at 400°F (200°C) for 18 to 20 minutes until deep golden brown and fully puffed.

Cool on the baking sheet for 5 minutes, transfer to a serving plate, and sift the 2 tbsp powdered sugar over the top before serving warm.