Heat 1 tablespoon olive oil in a large cast iron skillet over medium high heat. Add ground beef and cook until beef has browned, about 3-5 minutes, making sure to crumble the beef as it cooks; stir in taco seasoning. Drain excess fat; set aside.
Heat tortillas according to package instructions.
Heat nacho cheese according to package instructions.
Working one at a time, place ground beef mixture in the center of each tortilla. Top with nacho cheese and tostada shell. Spread sour cream in an even layer over the tostada shell; top with lettuce, tomato and cheese. Repeat with remaining tortillas.
Fold the edges up and over the center. Continue to work your way around the tortilla, folding as tight as possible.
Heat remaining 1 tablespoon olive oil in a large cast iron skillet. Place wrap seam-side down and cook until the underside is golden brown, about 2 minutes. Flip and cook wrap on the other side, about 1-2 minutes longer.