Preheat oven to 350 degrees. Cut down the center of the Hawaiian buns and place the bottom in a baking pan. You can also just buy the Hawaiian Slider Buns to make this easier. Grate about 2 tablespoons of onion and set aside, juice and all. Chop the remaining half of the onion. Combine mayonnaise, grated onion and juice, sugar, sweet pickle relish, 1/2 teaspoon of salt, vinegar, mustard, smoked paprika, and onion powder in a bowl and combine well.

In a skillet, brown ground beef over medium heat, add chopped onion, Worcestershire sauce,remaining salt, pepper, and cook for a minute or so. Remove from heat and stir in 1/2 cup of grated cheese and 2/3 cup of the sauce.