Preheat oven to 375°F (190°C) and grease a 9x13 inch casserole dish.
In a large skillet over medium heat, sauté the onion and red bell pepper in olive oil for 4 to 5 minutes until softened.
Add the minced garlic and cook for 1 more minute until fragrant.
Add the chopped spinach and cook just until wilted, then remove from heat.
In a large mixing bowl, combine cooked chicken, uncooked rice, sautéed vegetables, crumbled feta, shredded mozzarella, oregano, thyme, salt, and black pepper.
In a separate bowl, whisk together whole milk, sour cream, and chicken broth. Pour this mixture over the chicken and rice mixture and stir until fully combined.
Transfer the mixture into the prepared casserole dish and smooth the surface.
If using, mix breadcrumbs with olive oil and sprinkle evenly over the casserole.
Cover with aluminum foil and bake for 30 minutes.
Remove the foil and bake for an additional 15 minutes until the casserole is bubbly and the top is golden brown.
Allow the casserole to rest for 5 to 10 minutes before serving.