Pat the duck leg quarters completely dry with paper towels. This is the most important step for crispy skin, so take your time and make sure there is no moisture left on the surface.
Using a sharp knife, score the skin in several places through the fat layer but not into the meat. This helps the fat render evenly during cooking.
In a small bowl, mix together the salt, black pepper, garlic powder, smoked paprika, dried thyme, and ground ginger. Rub the olive oil all over the duck legs, then season them generously on all sides with the spice mixture. For the best results, season the legs and let them sit uncovered in the refrigerator for at least 1 hour or up to overnight.
Preheat the air fryer to 350 degrees F. Place the duck legs in the basket skin-side down. Make sure they are not overlapping so air can circulate freely.
Cook for 15 minutes skin-side down. This initial phase renders out much of the fat. Carefully drain any excess fat from the drip tray if it accumulates.
Flip the duck legs skin-side up. Continue cooking at 350 degrees F for another 15 minutes.
Increase the temperature to 400 degrees F and cook for a final 5 to 8 minutes until the skin is deeply golden, shatteringly crispy, and the internal temperature at the thickest part of the thigh reads at least 175 degrees F.
Transfer the duck legs to a plate and let them rest for 5 minutes before serving. The skin should crackle when you press it. Serve with roasted vegetables, a fresh green salad, or creamy mashed potatoes.