Form 6 somewhat-thin patties from the beef and sprinkle with salt and pepper. Fry the patties over medium to medium-low heat in a large skillet, 3 to 4 minutes per side.
Onto each half of a burger bun, place a cooked patty. Top with 2 to 3 tablespoons grated Cheddar and a pile of hot chili.
In a large, heavy pot, brown the ground beef with the garlic over medium heat until the beef is totally cooked, 8 to 10 minutes. Drain off most of the excess fat, leaving a little behind for moisture and flavor. Add the tomato sauce, tomato paste, chili powder, cumin, oregano, salt and cayenne. Stir together well, cover the pot and reduce the heat to low. Simmer for 1 hour, stirring occasionally; if the liquid level seems low, add up to 1 cup water to keep it from burning.
After an hour, stir in the kidney and pinto beans. In a small bowl, combine the masa harina with 1/2 cup water and stir together with a fork until it's smooth. Pour the masa mixture into the chili. Stir together well, then taste the chili and adjust the seasonings. Simmer the chili for another 10 minutes to thicken, then turn off the heat and let it cool.
Fill freezer bags with 2-cup portions and freeze them flat for easy stacking (or freeze in other freezer-safe containers).