Preheat the oven to 350 F. Grease a 9×13-inch baking dish or two 9x9 pans if you’re making one for now and one for later.
Place potatoes in a large pot of cold water over medium-high heat. Bring to a boil, reduce heat, and simmer. Cook potatoes for 15 minutes, or until tender.
Drain potatoes. Then mash with milk and butter; add salt and pepper and set aside briefly.
Meanwhile, in a large, deep skillet, cook meat until just about cooked through. Drain and return to skillet. Add onion and garlic. Cook until onion is tender, about 5 minutes
Stir in barbecue sauce, mustard, brown sugar, and liquid smoke.
Transfer meat mixture to prepared casserole dish.
Top with corn, scattering evenly over the top.
Carefully spread the mashed potatoes over the top and sprinkle with cheese.
Bake for 30-40 minutes, or until potatoes are nicely browned and meat mixture is bubbling.
Serve warm or cool completely and wrap tightly to freeze for later.
Reheat thawed casserole at 350 F for 25-30 minutes.