Rub the steak with the cut sides of the garlic. Brush the steak on both sides with the worcestershire sauce. season with salt and pepper. Set Aside at room temperature. quarter the potatoes, then cut into 1/4 inch thick slices.
In frying pan heat 2 tbs. of the oil over med-high heat. Add the onion and potatoes. Cook tossing for 1 to 2 minutes to lightly coat the potatoes with oil. Then continue to cook, turning only occasionally until the slices are nicely browned, about 5 minutes, Season with salt and pepper. Remove to a bowl cover with foil.
Wipe the pan clean, no need to rinse. Add the remaining oil to the pan and heat about 1 minute. Add the steak, cover, and cook undisturbed for 3 minutes, until browned on the bottom. Turn over, cover, reduce heat to medium, and cook until browned on the second side and rare in the center. set steak on cutting board. Pour off oil and wipe out the pan.
Add the butter to the pan and set over medium heat. Cook eggs as you like. Slice steak in wide slices on an angle. Plate steak, eggs, and potatoes.