In a medium bowl, combine mayonnaise, mustard, lemon juice, sugar, onion powder, and garlic powder. Mix until smooth and creamy, then set aside.

Heat a skillet over medium heat and melt 1 tablespoon of butter. Add the sliced onions and cook for 5-7 minutes, stirring occasionally, until they are golden brown and fragrant.

In the same skillet with the leftover butter and onions, add your steak patty or shaved steak. Cook for about 3-4 minutes per side until the meat is browned and cooked to your liking.

In a small bowl, whisk together one large egg and 1 tablespoon of milk until well combined. Pour this mixture into the skillet, using the remaining butter. Cook the eggs over medium heat for about 2-3 minutes until just set.

Toast your plain bagel halves until golden brown. Spread a generous layer of breakfast sauce on each half, then layer the bottom half with steak, golden caramelized onions, scrambled eggs, and a slice of melted cheese.