In a small bowl, mix mayonnaise, Dijon mustard, Dill, lemon juice, and steak sauce. Place bowl in the refrigerator to chill until ready to use.
Season the steak slices with Worcestershire sauce, steak seasoning, and garlic powder.
Heat a skillet or griddle over medium-high heat. Cook diced onions in olive oil over medium- heat until tender, about 5 minutes. Remove cooked onions from skillet and set aside.
Over medium-low heat, cook the steak slices for about 2-3 minutes on each side until cooked to your liking. Set aside.
Slice the bagels in half and lightly toast them.
In the same skillet used for the steak (add a bit more butter or olive oil if needed), melt the butter over medium heat. Cook eggs to your liking, I whisked beforehand and cooked until they were a scrambled texture.
Spread a generous amount of sauce on both halves of each toasted bagel.
Place cooked egg on bottom of the bagel, top with steak, cooked onions, and a slice cheese. Top with the other half of the bagel and serve.
Enjoy!