In a small bowl, combine the chili powder, cumin and 1 teaspoon salt. Stir until well mixed.
Divide the ground beef into 4 equal sections, about 6 ounces each. Gently form the meat into thick disks, then place on a piece of wax paper. Press the patties until they're about 1/2-inch thick and 6 inches in diameter. Sprinkle each patty on both sides with the spice mix, using about 1/2 tablespoon per burger. Cut each patty in half, giving you 8 pieces.
Heat a 10-inch cast-iron skillet over medium heat for 3 minutes. When the skillet is hot, add 1 tablespoon of the oil and 4 of the patties. Cook until the meat is browned half of the way up the side, 2 1/2 to 3 minutes. Flip and cook on the other side. Place a half-slice of cheese (torn into a few pieces so it fits on the burger) to cover the patty and melt over the top. Cook until the patty is well-browned on the bottom, another 2 1/2 minutes. Remove the burgers to a plate, tent with foil, to allow the juices to redistribute, at least 5 minutes. Scrape out any crusty bits on the bottom of the skillet and pour off the extra grease. Add the remaining tablespoon of oil and repeat the process for the remaining 4 patties.
If using hard taco shells, place them on a baking sheet and warm in the oven for about 5 minutes. If using soft tortillas, wrap the stack of 8 in foil and warm for 5 minutes.
Line the center of each taco with some lettuce, insert a patty and 2 tomato slices, then top with 1 teaspoon salsa and some sour cream, and serve.
