Prep the oven and pan: Heat oven to 400°F (200°C). Lightly grease a 9x13-inch baking dish or similar.
Season the chicken: Pat chicken dry.
Toss with 1 tablespoon olive oil, 1/4 teaspoon salt, pepper, smoked paprika, and onion powder. Set aside.
Par-cook the green beans: If using fresh beans, microwave or blanch 3–4 minutes until just crisp-tender, then drain well. If using frozen, thaw and pat dry.
This helps prevent a watery bake.
Soften the aromatics: In a skillet over medium heat, warm 1 tablespoon olive oil. Cook onion 4–5 minutes until translucent. Add garlic and cook 30 seconds until fragrant.
Remove from heat.
Make the sauce: In a bowl, whisk Greek yogurt, chicken broth, Dijon, thyme, lemon juice, and 1/4 cup Parmesan. Taste and adjust salt and pepper. The sauce should be savory and a little tangy.
Assemble: Add green beans and sautéed onions/garlic to the baking dish.
Scatter seasoned chicken over the top. Pour the sauce evenly over everything and gently toss to coat.
Add cheese: Sprinkle remaining 1/4 cup Parmesan and the mozzarella (if using) over the surface.
Bake: Cover loosely with foil and bake 15 minutes. Remove foil and bake another 10–15 minutes, until the chicken is cooked through (165°F/74°C internal temp) and the top is lightly golden.
Rest and garnish: Let sit 5 minutes so the sauce thickens.
Finish with chopped parsley or chives for freshness.
Serve: Spoon into bowls as-is, or pair with quinoa, brown rice, or roasted potatoes if you want extra carbs.