Heat the oven to 400°F (205°C) and set a rack in the middle. The oven is ready when it reaches 400°F, usually after 10 to 15 minutes.

Brown the beef. Heat a 12-inch skillet over medium-high, add the beef, and break it into small pieces with a wooden spoon. Cook for 6 to 8 minutes, until no pink remains and some pieces have browned on the pan. Food safety: USDA recommends cooking ground beef to an internal temperature of 160°F, and color alone is not a reliable guide. Wash your hands, the spoon, and anything the raw beef touched.

Spoon off the fat. Tilt the pan and remove all but about 1 tablespoon. The beef should look moist without sitting in a puddle.

Cook the onion in the pan. Stir often for 4 to 5 minutes, until the pieces are soft and translucent with a few browned edges.

Stir in the garlic, tomato paste, smoked paprika, and pepper. Cook for 1 minute, until the paste darkens to a brick color and smells sweet.

Add the soup and milk. Stir until smooth, then simmer for about 2 minutes, until the sauce bubbles with no white streaks. Taste it and add a pinch of salt only if it needs one.

Take the skillet off the heat and stir in the frozen peas and carrots and 1 cup of the cheddar. The cheese should mostly melt into the sauce while the mixture is still steaming.

Scrape the filling into a 9x13-inch (3-quart) baking dish and spread it level, corners included. You should see no bare spots.

Line up the frozen tots in tight rows, sides touching, in a single layer. Little filling should show between them.

Bake uncovered on the middle rack for 30 minutes. Golden tots on top and sauce bubbling around the rim mean it is ready for the last cheese.

Sprinkle the remaining 1 cup cheddar over the tots and bake for 5 more minutes. The cheese should be melted and browning in spots, and an instant-read thermometer pushed into the middle should show 160°F.

Let the casserole rest for 10 minutes. The filling should stop bubbling and firm up enough that a cut square holds its shape.