Heat the oven: Preheat to 375°F (190°C). Lightly grease a 9x13-inch baking dish.
Prep the broccoli: If using fresh, steam or blanch for 2-3 minutes until bright green and just tender. If frozen, thaw and pat dry.
You want it crisp-tender, not mushy.
Cook the turkey: Warm 1 tablespoon oil in a large skillet over medium-high heat. Add ground turkey and break it up with a spatula. Season with a pinch of salt.
Cook until no longer pink and lightly browned, 5-7 minutes. Transfer to a bowl and set aside.
Sauté aromatics: In the same skillet, add remaining oil and the diced onion. Cook 3-4 minutes until softened.
Stir in garlic and cook 30 seconds until fragrant.
Build the sauce base: Sprinkle flour over the onions and stir for 1 minute to form a paste. Slowly whisk in chicken broth, then milk. Simmer 2-3 minutes, stirring, until slightly thickened.
Season it right: Add salt, pepper, onion powder, smoked paprika, and thyme.
Taste and adjust. You want it well-seasoned now.
Make it creamy and cheesy: Remove from heat. Stir in Greek yogurt (or sour cream), 1 1/2 cups cheddar, and Parmesan if using.
Mix until smooth and melty.
Combine: Fold in the cooked turkey and broccoli until evenly coated. Transfer the mixture to the prepared baking dish and spread into an even layer.
Top it: Sprinkle the remaining 1/2 cup cheddar over the surface. If using a crunchy topping, toss panko with melted butter and scatter evenly on top of the cheese.
Bake: Bake 18-22 minutes, until the edges bubble and the top is golden.
For extra color, broil 1-2 minutes at the end, watching closely.
Rest and serve: Let the bake rest 5-10 minutes before serving so it sets. Garnish with chopped parsley or chives if you like.