Well Done with Ketchup is the only way to eat steak. Everybody knows this. We've come to this near unanimous decision many times here.
When I do steak and eggs with left over medium rare steak cut into pieces and scrambled with the eggs ketchup does make a nice garnish.
1) Take left over steak and brown in skillet with butter. Cut steak into bite sized pieces for yummy browning. Shouldn't take but a few minutes. The goal is to get the most surface area and browning possible, that's good eats.
2) Pour in scrambled eggs and cook, making sure they are still moist and slightly runny.
If you like put in green pepper, onion before browning steak and don't forget the salt/pepper. Dice tomatoes do wonders as well.