Melt 1 tablespoon of butter in a skillet over medium heat. Add the onion, salt, and pepper. Cook until onions are soft, about 5 minutes.
Increase the heat to medium-high and add the steak to the pan. Saute for 4-5 minutes, or until the steak is browned and cooked through.
Add the Worcestershire sauce, garlic powder, and remaining butter to the pan. Stir to combine. Meanwhile, cut the bagels in half and place them on a baking sheet. Bake for 3 minutes or until lightly toasted.
Heat a separate skillet over medium-high heat. Crack the eggs into the pan and cook for 2-3 minutes, or until desired doneness is achieved.
Place one egg on each bagel half, followed by cheese slices and steak slices. Top with remaining bagel halves and serve with steak sauce.