Preheat the oven to 375 degrees F (190 degrees C).

Place potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 15 minutes. Drain and transfer potatoes to a large bowl. Mash potatoes with 1 tablespoon butter using a potato masher or fork; season with salt and pepper.

Melt 1 tablespoon butter in a large skillet over medium heat. Cook and stir beef in the hot skillet until browned and crumbly, 5 to 7 minutes; drain and discard grease. Stir onion soup mix, chicken bouillon, and beef bouillon into ground beef; simmer until flavors blend, about 2 minutes. Add water if mixture is too dry.

Spread ground beef mixture into the bottom of a 2-quart casserole dish; top with corn, carrots, and peas. Spoon mashed potato mixture over vegetable layer; sprinkle with paprika.

Bake in the preheated oven for 20 minutes. Sprinkle Cheddar cheese over mashed potato layer; continue baking until cheese is melted and bubbling, about 10 more minutes.