Prep the broccoli: Cut into small, bite-size florets so they cook quickly. Rinse and set aside.
Shred the cheeses if not pre-shredded.
Brown the turkey: Heat the oil in a large skillet over medium-high heat. Add onion and cook 3 minutes until softened. Stir in garlic for 30 seconds.
Add ground turkey, 1/2 teaspoon salt, and pepper. Cook, breaking it up, until no longer pink and lightly browned, 5–7 minutes.
Season it up: Sprinkle in smoked paprika, Italian seasoning, and red pepper flakes if using. Stir and cook 1 minute to bloom the spices.
Steam-sauté the broccoli: Add broccoli and chicken broth.
Stir, then cover and let steam 3–4 minutes until bright green and crisp-tender. Uncover and let excess liquid simmer off for 1 minute.
Make a quick sauce: In a small bowl, whisk milk, Dijon, remaining 1/2 teaspoon salt, and cornstarch until smooth. Pour into the skillet and stir.
Reduce heat to medium and cook 2–3 minutes, until slightly thickened.
Add the cheese: Turn heat to low. Stir in cheddar and Parmesan by the handful, letting each addition melt before adding more. If using Greek yogurt or sour cream, fold it in now.
The mixture should be creamy and coat the turkey and broccoli.
Finish and taste: Squeeze in a touch of lemon juice to brighten the flavors. Taste and adjust salt, pepper, or mustard as needed.
Serve: Sprinkle with fresh herbs if you like. Serve as is, or spoon over rice, cauliflower rice, or quinoa for a heartier bowl.