Prep the oven and pan: Preheat your oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish with olive oil or nonstick spray.
Season the chicken: Pat the chicken dry.
Toss with 1 tablespoon olive oil, 1/2 teaspoon salt, 1/2 teaspoon pepper, and the smoked paprika if using. Set aside.
Soften the aromatics: Heat the remaining 1 tablespoon olive oil in a large skillet over medium heat. Add the onion and a pinch of salt.
Cook 3–4 minutes until softened. Stir in garlic and cook 30 seconds until fragrant. Remove from heat.
Make the creamy base: In a large bowl, whisk together the chicken broth, sour cream (or Greek yogurt), condensed soup, Dijon, onion powder, and garlic powder.
Stir in the cooked onion and garlic. Taste and adjust salt and pepper as needed.
Layer the bake: Add the broccoli and chicken to the baking dish. Pour the creamy mixture over the top and stir gently to coat everything.
Sprinkle 1.5 cups cheddar and the mozzarella evenly over the surface.
Top with crunch: In a small bowl, mix the breadcrumbs with the melted butter and a pinch of salt and pepper. Scatter evenly over the cheese. Finish with the remaining 1/2 cup cheddar.
Bake: Cover loosely with foil and bake for 20 minutes.
Remove the foil and bake another 15–20 minutes, until the chicken is cooked through (165°F/74°C at the thickest pieces), the sauce is bubbling, and the top is golden.
Rest and garnish: Let the bake rest for 5–10 minutes to set. Sprinkle with chopped parsley or chives for a fresh finish.
Serve: Spoon into bowls or plates. It pairs nicely with rice, quinoa, or buttered noodles to catch all that creamy sauce.