Sprinkle the steaks on both sides with salt and pepper.
Set a heavy skillet (cast iron is ideal) over medium-high heat, add a drizzle of oil and cook the steak for about 5 minutes per side for medium-rare.
Set aside and cook the eggs in the same skillet—however you like them.
Meanwhile, in the bowl of a food processor pulse the cilantro, parsley, shallot, jalapeño, garlic, vinegar, oregano and a big pinch of salt until well blended.
With the blender running, add the olive oil until the mixture is well-blended and saucy.
Slice the steak across the grain and serve with the eggs, drizzled with chimichurri.