Preheat oven to 425º.
Combine quinoa and chicken broth in a small saucepan and bring to a boil. Lower to a simmer, cover the saucepan with a lid, and cook for 14 minutes, or until all of the liquid has been absorbed. Let quinoa rest, covered, for 5 minutes, then fluff with a fork.
Place broccoli in a large (12-inch) ovenproof skillet. Drizzle with 1 Tbsp of oil and sprinkle with a pinch of salt and a few cranks of black pepper. Toss to coat. Arrange broccoli in a single layer in the skillet. Transfer to oven and roast for 13 to 15 minutes, until tender and lightly browned in spots. When you take broccoli out of the oven, reduce temperature to 375°.
While broccoli is roasting, heat remaining 1 Tbsp oil in a small skillet over medium heat. When oil is hot and shimmering, add garlic and cook for about 2 minutes, until golden brown. (Be careful not to burn garlic! If it looks like it’s browning too quickly, turn down heat.) Stir in bread crumbs and red pepper flakes (if using) and cook for 2 to 3 minutes, until crumbs are nicely toasted and have darkened a shade in color. Transfer bread crumbs to a small bowl.
Grate half mozzarella ball on large holes of a box grater. Slice remaining half into very thin rounds. (The rounds don’t need to be perfect—they’re going to melt!)
Add chicken, cooked quinoa, 2 cups of marinara sauce, and grated mozzarella to the skillet with broccoli. (Be careful, the skillet is HOT!) Fold everything together with a spatula until well-combined. Taste and season with a little salt and pepper if necessary. Smooth top of the filling with a spatula. Spread remaining ½ cup marinara sauce on top, then add sliced mozzarella cheese and sprinkle with Parmesan cheese and garlicky bread crumbs. Bake for 20 to 25 minutes, until the cheese has melted and topping is lightly browned.
Let rest for 10 minutes. (Trust me, you will burn your tongue!) Serve warm, topped with fresh basil, if you like.