Mince or grate 2 garlic cloves and place in a medium bowl or resealable plastic bag. Finely grate the zest of 1 medium lemon. Add half the zest to the garlic and reserve the remaining zest and lemon.
Add 4 chicken thighs, 1 tablespoon of the olive oil, 2 teaspoons dried oregano, and 1 teaspoon of the kosher salt to the bowl. Toss with your hands to combine well and rub the seasoning into the chicken. Cover and refrigerate at least 30 minutes or ideally overnight. Meanwhile, soak the potatoes.
Cut 1 1/2 pounds Yukon Gold potatoes in half lengthwise. Cut each half into 3 or 4 wedges. Place the potatoes in a large bowl, cover with cool water, and let soak for however long you let your chicken marinate (refrigerate if soaking overnight).
Heat an air fryer to 400ºF. Place the chicken in the basket in a single layer skin-side down. Air fry for 10 minutes. Flip the chicken and air fry until crispy and an instant-read thermometer in the thickest piece registers 165ºF, 12 to 15 minutes more. Meanwhile, drain the potatoes in a colander and pat very dry with towels. Place in a large bowl, add the remaining 1 tablespoon olive oil and 1 teaspoon kosher salt, and toss to coat.
When the chicken is ready, transfer to a platter and tent loosely with aluminum foil to keep warm. Place the potatoes into the air fryer basket in an even layer. Air fry for 20 to 25 minutes, taking the basket out and tossing the potatoes often, until crispy and golden brown. Meanwhile, coarsely chop a handful of fresh dill fronds (about 1/4 cup). Cut the zested lemon into wedges.
When the potatoes are ready, sprinkle with the dill and reserved lemon zest and toss to combine. Transfer the potatoes to the platter with the chicken and serve with the lemon wedges.
