Heat the oven: Set to 375°F (190°C).
Lightly grease a 9x13-inch baking dish.
Cook the pasta: Boil in salted water until very al dente (1–2 minutes shy of package time). Drain and set aside.
Make the roux: In a large pot, melt butter over medium heat. Stir in flour and cook 1 minute, whisking until lightly foamy.
Add minced garlic and cook 30 seconds.
Build the sauce: Gradually whisk in milk and chicken broth. Add onion powder, smoked paprika, dry mustard, salt, and pepper. Simmer 3–5 minutes, whisking, until thick enough to coat a spoon.
Stir in cheeses: Off the heat, add 1.5 cups cheddar, all the mozzarella, and Parmesan.
Whisk until melted and smooth.
Add Greek yogurt: Whisk in yogurt until the sauce turns glossy and creamy. Taste and adjust seasoning.
Combine: Fold in cooked chicken and the drained pasta. The mixture should be saucy; it will thicken in the oven.
Assemble: Transfer to the baking dish.
Sprinkle with remaining 1/2 cup cheddar. If using, top with panko and mist with olive oil spray.
Bake: Bake 18–22 minutes until bubbling at the edges. Broil 1–2 minutes to brown the top, watching closely.
Rest and serve: Let it sit 5–10 minutes so the sauce sets.
Scoop and enjoy.