Meanwhile, in a prep bowl, we combine the horseradish, mayonnaise, milk, some salt, and freshly ground pepper. We stir and taste for seasoning. We set this on the table.
We turn on our gas grill and allow it to heat up.
We put the ground sirloin into a bowl and with clean hands add a good amount of salt and freshly ground pepper. After mixing the meat and seasonings, we divide it into four balls. We flatten each ball into a good-sized hamburger patty.
We place the patties on the grill and cook on the one side for four minutes. We flip over with tongs, add the cheese, and continue to cook for another 3-5 minutes, depending on how well done we want the burgers. We serve the hamburgers on sesame buns with ketchup, the cooked bacon, and horseradish sauce.