Slice the onion into thin rings. Heat olive oil in a skillet over medium heat, then add the onions and sauté for 20-25 minutes until golden brown.

In a bowl, mix together mayonnaise and horseradish, seasoning with salt and pepper to taste. Refrigerate until ready.

In another skillet, cook bacon strips over medium heat for 10-15 minutes until crispy. Drain on paper towels.

In a bowl, combine ground beef, minced garlic, breadcrumbs, and egg. Season the mixture, shape into four patties, making a slight divot in the center.

Preheat the grill to high, reduce to medium-high, and cook the patties for 6 minutes on each side until internal temperature reaches 165°F.

Butter the insides of burger buns, toast them in a skillet over medium heat until golden brown.

Assemble the burgers by spreading horseradish mayo on the bottom buns, adding patties, crispy bacon, and caramelized onions, topping with the top bun.