Heat the oven to 375°F and cover a large baking sheet with parchment paper. Portion about 2 tablespoons of cheddar into separate mounds with space between them. Keep the mounds evenly sized so the finished cups set at a similar rate.
Bake the cheddar for about 6 minutes, then leave the rounds on the sheet for 1 minute. The centers should be bubbling and the outer edges should be just beginning to turn golden.
Coat the underside of a muffin tin with cooking spray, then lift each warm cheese round onto the inverted cups. Use a thin spatula if needed to check that the cheese disc holds together before moving it.
Set a second inverted muffin tin over the cheese-covered tin and let the shells cool for 10 minutes. The nested pans create flatter bottoms that sit steadily on a platter.
Use your hands to gently press the cheese around the inverted muffin cups if a second tin is unavailable. Handle the cheese only once it is warm and pliable rather than scorching hot.
Warm the olive oil in a large skillet over medium heat and cook the onion for about 5 minutes. Stir occasionally until it softens and smells sweet rather than raw.
Add the garlic, then crumble in the ground beef with a wooden spoon and cook for about 6 minutes. Break up larger pieces until the beef is no longer pink, then drain away the fat.
Return the drained beef to the skillet and stir in the chili powder, cumin, paprika, salt, and pepper. The meat should be evenly coated with spices and look moist without sitting in grease.
Move the cooled cheese cups to a serving platter and spoon in the seasoned beef. Finish with sour cream, avocado, cilantro, and chopped tomatoes.