Preheat the oven to 375°F (190°C).
Heat olive oil in a large skillet over medium-high heat.
Season the chicken pieces with salt and black pepper.
Add the chicken to the skillet and cook for 5-6 minutes, stirring occasionally, until cooked through and lightly browned. Remove chicken from skillet and set aside.
In the same skillet, add chopped onion and cook for 3-4 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant.
Add broccoli florets and chicken broth to the skillet. Cover and cook for 5 minutes until broccoli is tender-crisp.
In a large mixing bowl, combine Greek yogurt, shredded cheddar cheese, mozzarella cheese, Parmesan cheese, Dijon mustard, dried thyme, paprika, and crushed red pepper flakes. Mix well.
Add the cooked chicken, broccoli mixture (including any remaining liquid), and sautéed onions and garlic to the bowl with the cheese sauce. Stir until everything is evenly coated.
Transfer the mixture to a greased 9×13 inch casserole dish and spread evenly.
Sprinkle whole wheat breadcrumbs evenly over the top of the casserole.
Bake uncovered for 25-30 minutes, or until the casserole is bubbly and the top is golden brown.
Remove from oven and let rest for 5 minutes before serving.