In a large bowl stir to combine ¼ cup oil, soy sauce, honey, and 1 teaspoon pepper. Add steak, mushrooms, onion, and pepper and toss to coat. Cover and marinate, refrigerated, at least 30 minutes or up to 2 hours. If using bamboo skewers, soak in water while steak marinates.
Meanwhile, in a small bowl stir together remaining ¼ cup oil, vinegar, cilantro, garlic, pepper flakes, and remaining ¼ teaspoon pepper. Add salt to taste.
Prepare a hot two-zone grill fire or preheat a gas grill on high for 10 minutes, then turn one burner down to medium. Alternatively, preheat a grill pan or indoor grill over medium-high heat.
Thread beef and vegetables onto skewers. Place over direct heat or in grill pan or on indoor grill and cook, turning frequently, until browned all over, about 5 minutes. Transfer to cooler side of grill and cook, turning, until vegetables are tender, 5-10 minutes more.
Serve beef and vegetables with tortillas and cilantro sauce.