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.
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.
Serve immediately.
Notes
Soften the tortillas. Warm the tortillas first so they are easier to fold without cracking. Wrap the tortillas in a damp paper towel and microwave for about 30 seconds.
Add a patch. If the tortilla does not completely cover the filling, add a small extra piece of tortilla in the center, serving as a barrier (or patch) before folding.
Do not overstuff. Size matters! Overstuffing may sound like a good idea since the filling is the best part, but this can result in ripped tortilla and overspill.
Fold tightly. Fold the edges up and over the center as tightly as possible, cooking seam-side down first to seal the folds and preventing the filling from spilling out.