Prepare the Fries:

1. Slice the peeled potatoes into thin matchstick-style fries.
2. Toss the potato slices in a large bowl with olive oil and salt.
3. Lay fries in a single layer in the air fryer basket (work in batches). Air fry at 400°F (200°C) for 18 minutes, flipping halfway through.
4. Keep finished fries warm in the oven while cooking additional batches.

Make the Sauce:
5. In a small bowl, mix avocado mayo, Greek yogurt, ketchup, and relish. Stir until smooth and set aside.

Caramelize the Onions:
6. Heat a nonstick pan over medium-high heat with olive oil or oil spray. Add chopped onions and cook, stirring frequently, for 8–10 minutes until golden brown.
7. Add water, 1 tablespoon at a time, as needed to prevent burning and speed up cooking. Once golden and soft, remove from heat.

Prepare the Burger Patties:
8. Season the ground beef with salt, pepper, and garlic powder. Divide into 8 equal portions (1/8 lb each).
9. Gently form into thin patties, taking care not to overwork the meat.

Cook the Patties:
10. Heat the pan used for the onions over medium-high heat. Place the patties in the pan and cook for 1–2 minutes per side.
11. Flip the patties, add a slice of cheese to each, and cook for another minute until the cheese melts.

Assemble the Burgers:
12. Spread the sauce on the inside of each bun.
13. Layer as follows: bottom bun, burger patty, caramelized onions, another burger patty, more onions, lettuce, tomato, and the top bun.

Serve:
14. Serve immediately with the air-fried fries for a fast-food-style meal at home.