Preheat the oven to 400°F. Grease four individual casserole dishes with cooking spray, oil or butter. Set aside.
Set a large skillet over moderate heat. Once the pot is hot, add 2 tablespoons butter. Stir in the onion and garlic and cook until softened, about 5 minutes. Season with crushed red pepper flakes, dried basil, dried oregano and a large pinch of salt and pepper. Add the ham and cook until just starting to brown.
Add the remaining 2 tablespoons butter and allow to melt. Sprinkle in the flour and cook, stirring often, for about 30 seconds or so. Stir in the chicken stock and milk. Cook over low heat until thickened, about 10 minutes. Stir in the broccoli and cook for another 5 minutes. Turn off the heat and stir in the cheese until melted through.
Divide the mixture evenly between the prepared baking dishes and set aside.
Dust a work surface with flour and roll out the pie dough into a large circle about 1/4-inch thick. Cut out four large circle that are slightly larger than the baking dish. Make 4 slits on each and then place on top of the pot pie filling. Brush the top with egg wash and sprinkle with salt and pepper.
Place on a baking sheet and bake until deep golden brown and bubbly, for 25 to 30 minutes. Remove from the oven and allow to cool for 10 minutes before serving. Enjoy!