Step 1: Preheat your oven to 400°F (200°C). Line a large baking sheet with parchment paper.
Step 2: On a lightly floured surface, carefully unfold the thawed puff pastry sheets. Gently roll each sheet into a roughly 10×10 inch square.
Step 3: Using a sharp knife or pizza cutter, cut each pastry sheet into four equal squares. You will have 8 squares in total. Optionally, gently score a 1/2-inch border around the edges of each square, being careful not to cut all the way through.
Step 4: Transfer the pastry squares to the prepared baking sheet.
Step 5: In a medium bowl, combine the diced mango, granulated sugar, lime juice, cornstarch, and vanilla extract. Toss gently until the mango pieces are evenly coated.
Step 6: Spoon about 2-3 tablespoons of the mango mixture onto the center of each puff pastry square, staying within the scored border if you made one.
Step 7: Brush the edges of the puff pastry squares with the egg wash.
Step 8: Sprinkle the turbinado sugar over the egg-washed edges.
Step 9: Bake for 20-25 minutes, or until the puff pastry is puffed, golden brown, and the mango filling is bubbly and slightly thickened.
Step 10: Carefully remove from the oven and let cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely. Serve warm or at room temperature.