Set a rack in the center of your oven and preheat to 350 degrees F. Spray a 9×13 casserole dish with nonstick spray.

Heat the olive oil and butter in a large pot over medium heat. Add the onion, salt, and pepper once the butter has melted.

Cook the onion for 8 to 10 minutes until soft and translucent. Stir in the garlic and cook for 30 seconds.

Sprinkle the flour over the top and stir continuously for at least 1 minute.

Slowly pour in the milk and broth, stirring constantly to prevent lumps. Bring to a simmer, then reduce heat and let bubble until thickened, about 5 minutes.

Turn off the heat and remove the pan. Stir in the veggies, Greek yogurt, half of the cheddar cheese, mozzarella, Dijon, and thyme until smooth.

Stir in the shredded chicken and cooked rice.

Place the mixture in the prepared casserole dish. Top with the remaining cheese.

Bake until the cheese is melted and hot, about 15 minutes. Turn the oven to broil and cook until the cheese is lightly browned, about 3 additional minutes.

Remove from the oven and sprinkle with fresh parsley or thyme. Let rest for 5 minutes, then serve hot.