Preheat oven to 350°F. Heat a large skillet over medium-high heat and melt the butter. Add the ground beef and chopped onion, season with salt and pepper, and cook — breaking up the meat with a spatula — until no pink remains, about 8 minutes.
Using a slotted spoon, layer half of the cooked beef into the bottom of a 9x13-inch baking dish, draining away excess liquid. Spread half of the vegetables on top, season with salt and pepper, then pour one can of cream of mushroom soup over the surface and spread evenly.
Repeat with the remaining beef, vegetables, seasoning, and second can of soup, spreading the final soup layer as evenly as possible.
Arrange the frozen Tater Tots in a single layer over the top of the casserole, placing them in straight rows to cover the entire surface.
Bake uncovered for 45 minutes, or until the Tater Tots are well browned and the casserole is bubbling around the sides. Let cool slightly before serving.
Serve with ketchup if desired. Store leftovers in an airtight container in the refrigerator for up to 3 days. Reheat in the microwave or in a 350°F oven covered with foil for about 15 minutes.