Cut onions into thin slices, crosswise. Heat a large skillet with butter and olive oil. When the butter foams, add the sliced onions and toss to coat. Cook on medium heat, stirring occasionally until golden brown. Season with salt and black pepper to taste. These will be cooking while you prep the sauce and the patties.
For the burger sauce:
Mix mayonnaise, ketchup, garlic powder, and chopped pickles in a small bowl. Set aside.
For the sliders:
Preheat the air fryer.
Mix ground beef, Worcestershire sauce, Dijon mustard, onion powder, garlic powder, and salt and pepper in a large bowl. Use your hands to combine.
Form meat mixture into 8 meatballs that are the same size and weight. Press them out with your palms to form small patties.
Spray the preheated air fryer basket with nonstick cooking spray. Place patties in the basket. It's okay if they are touching, just not overlapping. Cook in batches if necessary.
Air fry patties at 380 degrees F for 5 to 7 minutes depending on desired doneness. I recommend cooking burgers well done with an internal temperature of 160 degrees F.
Top the patties with a slice of cheese that's been cut in half and folded over. Air fry for another minute to melt the cheese.
Remove sliders to a plate and toast buns in the air fryer for 1-2 minutes, if desired.
Place patties on the bottom bun then top with caramelized onions and burger sauce. Add the top bun and serve.
Notes
Cook patties in a single layer. It's okay if the edges are touching, though.
Use a meat thermometer to get your cheese sliders perfectly cooked.
Ground chuck will render a good amount of grease in the bottom of the basket. Be sure to discard grease in the trash, not the sink drain.