Preheat the oven to 425 degrees F. Grease or line a baking sheet with parchment paper.
Saute the Taylor ham over medium-high heat until just starting to brown and crisp up. Remove from the heat and drain on paper towels.
Divide the pizza dough into 4 equal balls and roll each into an 8-inch circle. Place 1 slice of cheese onto half of each circle of dough. Top with 1/2 cup scrambled eggs, 1/4 cup Taylor ham and another slice of cheese. Fold the dough over the filling, stretching to fit, then align the edges and seal with the egg wash. Press the edges with a fork to seal. Place the hand pies on the prepared baking sheet. Brush the tops with egg wash and cut 2 slits in the top with a sharp knife. Bake until golden brown, 20 minutes.