Slice the onion into thin rings. Add to a skillet on medium heat with the olive oil and cook for about 20-25 minutes or until they're nicely browned. Stir them every few minutes so they don't burn.
Meanwhile, prepare the burger sauce by mixing the mayo, horseradish, and salt & pepper (I just used a spoon and a small bowl). Place in fridge until needed.
While the onions are cooking, you can fry the bacon in a separate pan until it's crispy (10-15 minutes).
Pre-heat grill to high heat.
Prepare the burgers. Using your hands, combine the burger ingredients, taking care not to over-handle them. I am quite generous with the salt and pepper. Form into four patties and make a divot in the middle of the burgers so they cook evenly.
Turn the grill down to medium-high heat. Place the burgers on the grill and cook for about six minutes (depends on thickness of burgers and the grill/BBQ you're using), then flip and cook for another six minutes or until they're cooked through.
My preferred method for toasting the insides of hamburger buns is to pre-heat a skillet on medium-high heat (on the stove) and then add the cut and buttered bun halves to the pan until they're toasted (takes a few minutes). You could always use the bacon fat skillet for some extra bacony deliciousness and fewer dishes. You could also toast them on your grill.
Assemble burgers by adding the sauce, burger patties, bacon, onions, and any other preferred toppings. Enjoy!