Preheat your oven to 375°F (190°C).

Cut the chicken breast into bite-sized pieces. Season with salt and black pepper.

In a large skillet, heat olive oil over medium heat. Add the chicken pieces and cook until browned on all sides. Remove from the skillet and set aside.

In the same skillet, add butter and melt it down. Add the finely chopped garlic and onions. Sauté until the onions are translucent and the garlic is fragrant.

Sprinkle the flour over the onions and garlic, stirring constantly for about 1 minute to cook the flour.

Gradually stir in the chicken broth and milk, whisking to combine and create a smooth sauce. Let it thicken slightly, about 3-4 minutes.

Return the chicken back to the skillet, stirring to coat with the sauce. Mix in 1/2 cup of grated cheddar cheese and the dried thyme. Check the seasoning and adjust if necessary.

Pour the chicken mixture into a casserole dish. Sprinkle the remaining cheddar cheese on top.

Bake in the preheated oven for 25-30 minutes until the top is golden and bubbly.

Let the casserole cool for a few minutes before serving.