Whisk sauce ingredients in a saucepan. Simmer 5 minutes over low, stirring. Set aside.
Cook bacon until crisp (air fryer 375°F, 8 to 10 min). Drain; save 1 tbsp fat.
Dip onion rings in buttermilk, then seasoned flour-panko mix. Repeat for a double coat.
Air fry rings at 400°F for 8 to 10 minutes, flipping and spraying halfway, until golden. Hold in a 200°F oven.
Form beef into four 6-oz patties, 1/2 inch thick, dimpled in the center. Season both sides.
Cook on a smoking-hot Blackstone or cast iron 3 minutes. Flip, add cheese, cook 2 to 3 minutes more.
Brush bun cut sides with butter or bacon fat; toast on the griddle 30 to 60 seconds.
Build: sauce on bottom bun, patty with cheese, 2 bacon strips, 2 onion rings, more sauce, top bun. Serve immediately.