Mexican tortas are traditionally served on pillowy, slightly sweet telera rolls typically found in Mexican panaderias. If you cannot find telera rolls, look for Portuguese rolls or any large, soft deli roll.
Mix the crema, cilantro and lime juice in a small bowl; season with salt and pepper. Combine the beef with 1/2 teaspoon each salt and pepper in a large bowl; mix well. Divide the mixture into 8 equal-size balls.
Heat a large nonstick skillet over medium heat. Lightly coat with cooking spray. Smash 4 of the beef balls into very thin patties. Add the patties to the skillet and cook, smashing them even more with a spatula, until browned, about 3 minutes. Flip the patties, top each with a slice of cheese and cook until the patties are cooked through and the cheese melts, about 2 more minutes for medium doneness. Wipe out the skillet, lightly coat with more cooking spray and repeat with the remaining beef and cheese to make 4 more patties.
Spread the crema mixture on the cut sides of the rolls. Place 2 patties in each roll with the salsa, lettuce, avocado and radishes. Serve with tortilla chips.