Heat oven to 350ºF. Grease 9"x13" casserole dish with 1 tbsp. butter; set aside. Cook rice according to package directions; set aside.
Heat remaining butter and oil in large skillet over medium-high heat. Add onions, sprinkle with cayenne pepper and cook until translucent, stirring occasionally, about 5 minutes. Add spinach; cook until heated through, about 5 minutes more; set aside.
In a large bowl, whisk together the eggs and the milk until well blended. Stir in 4 cups cheese, basil, parsley, thyme, reserved rice and reserved spinach mixture until combined. Pour rice mixture into prepared casserole dish; sprinkle with remaining cheese. Bake, uncovered, until cheese melts and begins to bubble, about 30 minutes.