Preheat oven to 375 F and line a baking sheet with parchment paper.
Unroll the pizza dough onto a cutting board and press into a rectangle. Use a pizza cutter to cut each side of the braid into 12 strips.
In the center of the dough, layer 4 slices of cheese, the shredded pork, relish, mustard, ham and then the remaining 4 slices of cheese. Fold the strips of dough over the filling, alternating sides.
In a small bowl, whisk the egg and water to make an egg wash. Brush over the braid. Bake for 15 to 17 minutes, or until golden brown on top.
In a small bowl, mix the melted butter, parsley and garlic powder, then brush over the warm braid.