Preheat oven to 400°F. Prepare muffin batter according to package directions; pour into lightly greased 8-inch square baking pan. Bake 20-25 minutes or until lightly browned. Cool completely.
Cut cornbread into 1-inch cubes; place in 13x9-inch baking pan. Bake 10-12 minutes or until golden brown. Transfer to lightly greased 2-quart casserole.
Melt butter in large skillet over MEDIUM heat. Add onion and thyme, if desired; cook 4 minutes or until onion is tender, stirring frequently. Spoon over bread cubes; top with sausage and corn.
Beat eggs, half-and-half, salt and pepper in small bowl with wire whisk until well blended; pour over ingredients in casserole. Gently press bread cubes into egg mixture until completely covered. Cover with foil.
Bake 1 hour or until knife inserted in center comes out clean, uncovering after 45 minutes. Let stand minutes before serving.