Combine chipotle, cumin, oregano, and salt in a small cup. Rub steak pieces with 1 tablespoon of the oil, then with spice mixture. Squeeze juice from lime half over steak pieces. Heat a stove-top grill pan over medium heat.
Heat the remaining 2 tablespoons oil in a large nonstick skillet over medium-high heat. Add onion, bell peppers, and chile; sauté 4 minutes. Add garlic and continue to sauté 4 to 6 minutes, or until crisp-tender. Remove from heat; stir in cilantro and season with kosher salt and pepper.
Grill steaks 3 minutes per side for medium-rare. Remove from grill; let rest 5 minutes. Slice against the grain and serve with pepper mixture, warm tortillas, and lime wedges.