Preheat oven to 400°F.* Set out a baking sheet.
On a lightly floured surface, roll out each sheet of puff pastry to a 10x10-inch square. Cut each into 4 squares for a total of 8 squares (about 5x5 inches each).
Set out a sheet of parchment paper (about the size of the baking sheet). Place one of the puff pastry squares onto the parchment. Leaving a 1-inch border around the edges, top the puff pastry square with the following: 2 slices ham, ½ cup cheddar cheese, 2 slices turkey, and ½ cup Swiss cheese. Brush the edges with egg wash.
Top with a second puff pastry square, stretching to fit and aligning the edges. Using a fork, crimp the edges to form a seal. Repeat with the remaining puff pastry squares. Carefully slide the parchment paper (with puff pastries) onto the baking sheet. (Alternately, you could prepare the puff pastries directly onto the parchment paper-lined baking sheet, carefully crimping the edges.)
Brush the tops of the puff pastries with egg wash. Then, cut three slits on the top to allow steam release.
Bake for 20-25 minutes, or until puffed and golden brown. Allow puff pastries to cool slightly before slicing and serving.
Serve warm, dusted with confectioners' sugar, with red raspberry preserves for dipping.