Step 1

Sprinkle steak with chili powder and season generously with salt and pepper. Heat 1 tablespoon oil in a large, heavy skillet (such as cast iron) over high until just smoking, 1 to 2 minutes. Working in batches, add steak and cook, flipping once, until well browned and just cooked through, 1 to 2 minutes a side. Transfer to a plate; tent with foil.

Step 2

Combine tomato and cilantro; season with salt and pepper. Blister tortillas over an open flame and wrap in a clean towel to keep warm. Heat a small nonstick skillet over medium and swirl in remaining 1 tablespoon oil.

Step 3

Add eggs to skillet, season with salt and pepper, and cook, stirring often, until just set, about 2 minutes; remove from heat. Slice meat against the grain, then chop into bite-size pieces. Serve in tortillas with eggs, tomato mixture, queso fresco, and more chili powder, with lime wedges alongside.