Form ground chuck into 1/3 pound balls and refrigerate for 30 minutes to firm up.
Thinly slice white onions with a mandoline, blot dry with paper towels, and refrigerate.
Make the Baconnaise sauce by combining mayonnaise, ketchup, mustard, bacon, Worcestershire sauce, apple cider vinegar, all-purpose rub, and red pepper flakes. Mix well and chill.
Cook bacon until crispy in a pan, chop finely, and divide portions for the sauce and burger toppings.
Heat avocado oil on a griddle over medium-high heat.
Place burger balls on the griddle and pile sliced onions on each. Smash down using a burger press and season with salt, pepper, and garlic.
Cook patties for 3 to 4 minutes, brush mustard on top, flip, immediately add pepper jack cheese, and cook for another 3 minutes until cheese melts.
Toast burger buns on the griddle while patties finish cooking.
Assemble burgers by spreading Baconnaise sauce on the bottom buns, stacking two patties with extra sauce, then topping with the toasted bun. Serve hot.