Combine lime juice, soy sauce, 1 tablespoon oil, garlic, chili powder, cumin, oregano, salt, and pepper in a bowl and whisk until well combined.
Pat the steak dry with paper towels, place in a zip-lock bag or glass dish, pour marinade over, and massage into the meat. Refrigerate for 1 to 4 hours.
While the steak marinates, finely dice white onion, roughly chop cilantro, and cut limes into wedges. Crumble cotija cheese if using.
Remove steak from refrigerator 20 to 30 minutes before cooking. Remove from marinade, shake off excess liquid, and reserve the marinade.
Heat cast iron skillet over medium-high heat for 2-3 minutes, add remaining 1 tablespoon oil, and sear steak for 2 minutes per side. Pour reserved marinade over and cook for 1-2 more minutes until desired doneness (130-135°F for medium-rare).
Transfer steak to cutting board, tent with foil, and rest for 5 minutes. Slice thinly against the grain, then chop into bite-sized pieces.
Warm corn tortillas in a dry skillet over medium heat for 30-45 seconds per side until pliable with light char spots. Stack two tortillas for each taco.
Place double-stacked tortillas on a plate, add a generous portion of chopped steak, and top with white onion, cilantro, cotija cheese (optional), and a squeeze of lime. Serve immediately with salsa verde on the side.