Preheat the oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish.
Prep the broccoli.
If using fresh, cut into small florets. Blanch in boiling water for 2 minutes, then drain well. If using frozen, thaw and pat dry to remove excess moisture.
Cook the aromatics.
Heat olive oil or butter in a large skillet over medium. Add diced onion and cook 3–4 minutes until softened. Stir in minced garlic and cook 30 seconds until fragrant.
Brown the ground chicken.
Add the chicken to the skillet. Season with salt, pepper, onion powder, garlic powder, and paprika. Cook, breaking it up with a spoon, until no longer pink and lightly browned, about 5–7 minutes.
Make the creamy sauce.
Sprinkle flour over the chicken and stir to coat. Slowly whisk in chicken broth, then milk. Simmer 2–3 minutes until slightly thickened and glossy.
Stir in the dairy.
Remove from heat. Fold in Greek yogurt or sour cream, 1 cup of shredded cheese, and 1/4 cup Parmesan. Taste and adjust seasoning.
Combine with veggies.
Add broccoli florets to the skillet. If using rice or quinoa, fold that in now. Mix gently until everything is coated.
Transfer and top.
Spoon the mixture into the baking dish. Sprinkle with remaining shredded cheese and remaining 1/4 cup Parmesan. If using, scatter breadcrumbs or crushed crackers on top for crunch.
Bake.
Place on the center rack and bake 18–22 minutes, until bubbly around the edges and the top is golden.
Rest and serve. Let the casserole sit 5–10 minutes to set. Garnish with chopped parsley or chives.
Serve warm.