Form the ground chuck into 1/3 pound balls and refrigerate for 30 minutes.
Slice the white onions as thin as possible, using a mandoline safely with the guard or gloves. Squeeze out excess water and refrigerate.
Crisp up the bacon, chop it, and set it aside.
Prepare the Baconnaise Sauce: Mix mayo, ketchup, mustard, bacon, Worcestershire sauce, apple cider vinegar, all-purpose rub, and red pepper flakes. Refrigerate.
Heat a griddle to medium-high heat. Apply avocado oil and place burger balls on the griddle, 2-3 inches apart. Add sliced onions on top and smash down with a burger press. Season with salt, pepper, and garlic.
Cook for 3-4 minutes, then add mustard on top, flip, and add pepper jack cheese. Cook until cheese melts, about 3 more minutes.
Toast burger buns on the griddle. Assemble the burgers with Baconnaise sauce on the bottom bun, double smash burgers, more Baconnaise sauce, and the top bun.