Heat 1 tablespoon of the oil in a large skillet over medium-high heat.
Season the steak with salt and pepper.
Cook the steak, 4 to 5 minutes each side.
Remove from skillet and let rest for 5 minutes, then slice.
Add the tomatoes to the skillet cut-side down, cook until browned, 2 to 3 minutes.
Add oil to the skillet, and cook the eggs covered to your desired doneness, 2 to 4 minutes.
Sprinkle the tomatoes and eggs with the oregano and salt and pepper.
Serve with the steak.