Brown the beef: Heat a large skillet over medium-high. Add the ground beef (and oil if using).
Cook, breaking it up, until browned and no pink remains, about 5–7 minutes. Spoon off excess fat if needed.
Add aromatics: Stir in the onion and cook until softened, 3–4 minutes. Add garlic and cook until fragrant, 30 seconds.
Season it up: Sprinkle in chili powder, cumin, smoked paprika, salt, and pepper.
Stir to coat the beef and onion.
Build the base: Add tomato paste and cook, stirring, 1 minute to toast it. Pour in the diced tomatoes with their juices and the water or broth. Stir well.
Soften the cabbage: Add the sliced cabbage in batches, tossing as it wilts.
Reduce heat to medium, cover, and cook 6–8 minutes, stirring once or twice, until cabbage is tender but not mushy. Adjust salt to taste.
Melt the cheese: Sprinkle cheese evenly over the mixture. Cover for 1–2 minutes, just until melted.
Finish with crunch: Turn off the heat.
Scatter the lightly crushed Fritos on top. Let them warm in the residual heat for 1 minute so they stay crisp.
Garnish and serve: Add green onions, cilantro, and jalapeños if you like. Serve hot with a dollop of sour cream or a dash of hot sauce.