Pat the steak dry to remove any moisture. Lightly coat with oil, then season with coarse salt and pepper. Let the steak rest at room temperature for 30-60 minutes.
In a large bowl, toss the quartered potatoes and diced onion with a light coating of oil, paprika, garlic salt, and onion powder. Begin cooking potatoes on medium-low heat with oil or butter as needed, using a dome to help them cook through.
Heat the griddle to high on the opposite side, adding a swirl of oil and butter. Sear the steak on one side for 3-5 minutes without moving, then flip to sear the other side, adding more butter if needed. Rotate the steak with tongs to sear the edges. Remove from heat just before reaching desired doneness and let it rest for 5-10 minutes with a dab of butter if desired.
Plate the potatoes and cook eggs to preference. Slice the steak and serve.
