Bring Yukon gold potato and water to cover to a boil in a large Dutch oven. Reduce heat, and cook 20 minutes or until tender; drain. Repeat procedure with sweet potato.
Beat Yukon gold potato at medium speed with electric mixer until mashed. Add half of milk, half of cheese, and 1 tablespoon butter, beating until smooth. Stir in onions, 1 teaspoon salt, and pepper. Spoon into a lightly greased 3-quart oval baking dish.
Beat sweet potato until mashed; add remaining milk, remaining cheese, and remaining 1 tablespoon butter, beating until smooth. Stir in remaining 1/2 teaspoon salt and thyme. Spread over Yukon gold potato mixture, and swirl gently with a knife. Cover and chill up to 8 hours, if desired.
Bake at 350° for 25 to 30 minutes or until thoroughly heated. Garnish, if desired. .