In a large skillet, over medium heat, saute the sausage, peppers, and onions. Cook, stirring until the sausage is cooked through completely and slightly crisp. Drain the sausage mixture, and set aside.
Roll the dough out onto a lightly floured, flat surface. Use a rolling pin to roll it out until it's almost doubled in size. Cut in half. Add both halves to a parchment paper lined baking sheet, so that one half is hanging over the edge, waiting for when you need to fold it over and seal.
Divide the salsa, and spread evenly over each half of the dough on the pan. Spread half of the sausage and pepper mix evenly over each pieces. Divide the eggs and spread half over each salsa covered piece of dough. Top each with 1/4 cup of the cheddar and 1/4 cup of ham.
Now's the fun part. Pull that other half of the dough hanging over the tray up and over the fillings. You want about 1/2-1" of just overlapping dough. Use your fingers to pull and pinch the dough together, or use the tines of a fork to seal the dough together.
Using a sharp knife, cut 3 slits in the top of each calzone. Use a brush to spread the melted butter evenly over each one. Sprinkle the 1/4 cup of cheese evenly out overtop each calzone.
Bake them at 350 degrees for 25 minutes, or until the dough's cooked and golden brown. Remove the calzones from the oven, let them rest 5 minutes, and slice and serve!