Add uncooked carne asada to large bowl. Add garlic, salt, pepper, balsamic vinegar, 1 tablespoon of fresh lime juice, orange juice, basil leaves, honey, olive oil, and 1/2 cup red onions to meat. Mix together completely and marinate 5 minutes.
Add marinated meat to grill on medium to high heat. Brush the marinade over meat and cook until well done.
Grill nopales leaves on both sides over medium heat, 5 minutes on each side.
Remove meat and nopales leaves from grill and slice in very thin pieces.
Warm tortillas on grill. Place warm tortilla on plates. Add carne asada to center of each tortilla.
Add to the center, remaining red onion, nopales, cilantro, green onions, remaining 1 tablespoons of lime juice, and salsa.