Preheat the Oven and Prepare the Baking Sheet: Adjust your oven rack to the middle position and preheat the oven to 400°F (200°C). Line a large, sturdy baking sheet with parchment paper or a silicone baking mat.

Prepare the Egg Wash and Brie: In a small bowl, whisk together the cold egg and the cold water until smooth. Set aside. Use a sharp knife to cut the chilled wheel of brie cheese into 12 small, roughly uniform cubes or triangles, leaving the rind intact.

Roll Out and Cut the Puff Pastry: Lightly dust a clean work surface with flour. Unfold the thawed puff pastry sheet and gently roll it out just enough to smooth creases, ensuring even thickness (approximately 1/8 inch). Use a ruler and a pizza cutter to divide the pastry sheet into 12 small, uniform squares or rectangles.

Fill the Pastry Squares: Place one small cube of brie cheese directly in the center of each pastry square. Spoon approximately 1/2 to 1 teaspoon of your chosen fruit jam directly on top of the brie cheese. Be careful not to overfill.

Seal the Edges: Lightly moisten the four edges of the pastry square with the prepared egg wash. Carefully fold two opposite corners of the square up over the filling, meeting them in the center. Pinch the edges together tightly to seal the filling inside, creating a small bundle or triangle shape. Repeat with all 12 pastries and transfer them to the prepared baking sheet, spacing them at least 1 inch apart.

Apply the Egg Wash and Toppings: Gently brush the entire surface of each assembled pastry with the remaining egg wash. If desired, immediately sprinkle the tops with turbinado sugar or chopped pecans.

Bake Until Golden: Place the baking sheet into the preheated 400°F (200°C) oven. Bake for 18 to 20 minutes, or until the pastries have puffed dramatically, and the surface is a deep, uniform golden brown color.

Cool and Serve: Remove from the oven. Allow the Brie and Jam Pastry Appetizers to cool on the baking sheet for a minimum of 5 to 10 minutes before serving. Serve warm.