Rub both sides of steak with garlic and cumin, then with 1 1/2 teaspoons oil and lime juice. Let stand while preparing peppers.
Heat 1 tablespoon oil in heavy medium skillet over medium-high heat.
Add onion and cook until beginning to brown, stirring frequently, about 6 minutes.
Add chiles and peppers and stir until heated through.
Add cream, then 3/4 cup cheese and stir until mixture thickens, about 1 minute.
Add oregano. Season with salt and pepper.
Heat 1 tablespoon oil in heavy large skillet over high heat.
Season steak with salt and pepper. Cook until brown, about 1 1/2 minutes per side for very rare.
Transfer to work surface. Halve across width, then cut against grain into thin slices.
Hold 1 tortilla over gas burner on low or place on electric burner on low until heated through, about 15 seconds per side. Place tortilla on work surface. Spoon 1/4 cup pepper mixture down center of tortilla. Top with 1/4 of meat. Roll up tortilla, enclosing filling.
Arrange in baking pan, seam side down. Repeat with remaining tortillas, 3/4 cup pepper mixture, and remaining meat.
Spoon remaining pepper mixture over tortillas.
Sprinkle with 1/2 cup cheese.
Bake uncovered until cheese melts, 5 to 10 minutes.