Preheat oven to 450 degrees. Very lightly brush a 10-inch cast iron skillet with olive oil.
Prepare Sauce:
Transfer tomatoes to a small bowl, discarding liquid. Using your hands, crush the tomatoes, leaving some small to medium-sized chunks.
Heat 2 teaspoons olive oil in a medium skillet over medium heat.
Add garlic, salt, and crushed red pepper flakes to pan, then saute until fragrant (about 30 seconds).
Stir tomatoes into skillet, then bring to a simmer and cook until thick (about 5 to 10 minutes).
Remove sauce from heat and season to taste with salt and pepper. Set aside.
Prepare Broccoli:
While sauce is cooking, place broccoli in a microwave safe dish with a lid.
Add 1 tablespoon water to dish, cover, and microwave for about 2.5 minutes, or until broccoli is just tender (do not overcook).
Sprinkle broccoli with salt to taste, then set aside.
Assemble pizza:
Mix together mozzarella, cheddar, and romano cheeses. Set aside.
Press dough into bottom and up the sides of the skillet. (Tip: if your dough is not cooperating, let it rest for a few minutes. Then stretch it some more, then let it relax again. Repeat this process until the dough covers the pan evenly).
Cover the dough with half the cheese.
Top cheese with the spinach and then the broccoli. Sprinkle the remaining cheese over the broccoli.
Dollop the sauce over the cheese (don't worry if it doesn't cover the whole pie).
Sprinkle feta cheese over top.
Bake until the crust is browned, about 25 to 30 minutes.
Remove pizza from oven, then let sit for 5 minutes.