Preheat the oven to 500°F. Position a rack at the lowest level in the oven and put a pizza stone on it.
Cook the bacon in a large skillet over medium heat, turning as needed, until almost crisp, about 10 minutes. Transfer the bacon to a paper towel-lined plate. Let cool, then crumble and set aside. Reserving the bacon drippings in the skillet.
Meanwhile, place the broccoli in a mesh strainer or fine colander and run cold water on it to thaw. Set it over a bowl to strain out excess water. Put it in a medium bowl, pour 2 tablespoons of bacon drippings over it, sprinkle with some salt and pepper and toss to coat; set aside.
Also, cook the eggs over medium heat until cooked.
Dust the work surface with a little flour. Put the parchment paper on a pizza peel or the back of a baking sheet. Halve the pizza dough and cover one half with a towel. Drape the other half over your fist and gently tug and turn it, letting the weight of the edges help stretch it thinner, until you have a round about ¼-inch thick and 12 inches across. Place the dough on the parchment and scatter with 1 cup of the Cheddar, then half the broccoli, leaving a 1-inch border. Slide the parchment onto the hot pizza stone and bake for 5 minutes.
After the pizza has baked for 5 minutes, rotate it and spread the scrambled eggs onto it. Scatter 1/2 cup of cheese and half the bacon on top. Bake until the pizza is browned and crisp on the bottom, about 5 minutes.
Transfer the pizza to a cutting board and let sit for 2 minutes.
Repeat with the other half of the dough and the remaining ingredients.
Slice and serve with crushed red pepper flakes or hot sauce.