Preheat oven to 375°F (190°C).
Sauté Onions: In a large pot, melt 2 tbsp butter over medium heat. Add diced onions and cook for 5 minutes until softened.
Add Garlic & Seasonings: Stir in garlic, thyme, and garlic powder. Cook for another minute.
Cook the Rice: Pour in olive oil, chicken broth, and rice. Stir to combine. Bring to a boil, then reduce heat to a simmer. Cover and cook for 15 minutes without stirring.
Let It Rest: Turn off heat and leave the lid on for 10 minutes. This allows any stuck rice to release from the pot.
Mix Ingredients: Stir in cream of chicken soup, sour cream, milk, Dijon mustard, cheddar cheese, Parmesan cheese, cooked chicken, and ham.
Assemble the Casserole: Transfer mixture to a lightly greased 9x13-inch casserole dish. Layer Swiss cheese slices on top. Cover and bake for 15 minutes.
Add Topping: Mix melted butter with breadcrumbs and sprinkle over the casserole. Bake uncovered for another 10 minutes until golden brown.
Let It Rest: Allow the casserole to sit for 5 minutes before serving.