Preheat & Prep: Preheat your oven to 375°F (190°C). Lightly coat a 9x13-inch baking dish with a small drizzle of olive oil.
Mix the Sauce: In a medium bowl, thoroughly combine the plain Greek yogurt, minced garlic, diced onion, Italian seasoning, smoked paprika, salt, black pepper, 1/2 cup of shredded mozzarella, and 1/4 cup of grated Parmesan cheese.
Layer the Pan: Place the cubed raw chicken breasts and fresh broccoli florets directly into the prepared baking dish. Drizzle with 1 tablespoon of extra virgin olive oil and toss lightly to coat.
Coat Evenly: Pour the creamy yogurt mixture over the chicken and broccoli. Use a flexible spatula to mix and spread the sauce evenly so every single piece is well-coated.
Add the Cheese Top: Evenly sprinkle the remaining 1/2 cup of mozzarella and 1/4 cup of Parmesan cheese over the top of the casserole.
Bake: Bake uncovered in the preheated oven for 25 to 30 minutes. The chicken should be cooked through (reaching an internal temperature of 165°F) and the cheese layer on top should be bubbling and beautifully golden brown.
Rest & Serve: Remove from the oven and let the bake rest for 5 minutes at room temperature before slicing and serving.