Preheat the oven to 400 degrees F. Line a large baking sheet with parchment paper.
In a small bowl, stir together mascarpone cheese, crushed gingersnap cookies and honey.
On a surface lightly dusted with flour, roll the one half sheet of store-bought puff pastry into a rectangle that's about ¼-inch thick. Cut the sheet in half to form two squares.
Using a level 1 tablespoon measuring spoon, lay the mascarpone mixture at even intervals on one square of puff pastry.
Lay one defrosted marionberry on the top of each mound of mascarpone.
Cover with the other puff pastry rectangle and, using your hands, gently press the top puff pastry sheet to form loosely around each mascarpone/marionberry mound.
Using a handheld circle ravioli cutter or a small, sharp knife, cut around each mound to form four “ravioli”.
Using a small metal spatula, lift the ravioli onto the prepared baking sheet, spacing them evenly. With a small sharp knife, cut two small slits in the ravioli to release steam while cooking.
In a small bowl, whisk together one egg white and 2 teaspoons water, and brush the surface of the ravioli with the mixture.
Sprinkle turbinado sugar evenly over the ravioli. Bake until the ravioli are golden brown, turning the baking sheet halfway through cooking, about 10 minutes. Place on a cooling rack for 5 to 10 minutes.
Place 2 ravioli on each plate and drizzle with the chocolate sauce. Serve immediately.