Preheat the oven to 375 degrees F. Line 2 baking sheets with parchment paper.
In a medium skillet, cook the onions in the butter over medium heat until translucent. Remove from the heat and cool. In a small bowl, combine the shredded cheeses.
Unroll both pie crusts and stack on top of each other on a clean work surface. Roll the crusts together to a 1/8-inch thickness. Cut twelve 3 1/2-inch circles from the dough, rerolling the dough as necessary.
Brush the edges of the circles with the egg wash, and fill each with 1 teaspoon onion, 2 teaspoons ham and 2 teaspoons cheese. Fold in half and crimp the edges to seal. Place on the prepared baking sheets. Cut 3 small slits on top of each to vent, and brush with the remaining egg wash. Bake until golden, 12 to 15 minutes. Serve with Honey-Mustard Dipping Sauce.
In a small bowl, whisk together the honey and mustards.