To spatchcock each quail, use sharp kitchen shears to cut along both sides of the backbone and remove it. Flip the quail breast-side up and press down firmly on the breastbone with the heel of your hand until you hear a crack and the bird lays flat.
In a bowl, whisk together the olive oil, minced garlic, lemon juice, thyme leaves, crushed rosemary, salt, and black pepper. Place the quail in a dish or large zip-top bag and pour the marinade over them, turning to coat completely.Let them marinate for at least 30 minutes at room temperature, or up to 4 hours in the refrigerator.
While the quail marinates, prepare the honey-lemon glaze by stirring together the honey, melted butter, lemon juice, and flaky sea salt in a small bowl. Set aside.
Preheat the air fryer to 380 degrees F for 3 minutes. Remove the quail from the marinade and place them skin-side down in the basket, making sure they do not overlap.
Cook for 8 minutes, then carefully flip the quail skin-side up using tongs. Cook for another 5 to 6 minutes until the skin begins to turn golden and crispy.
Brush the honey-lemon glaze generously over the skin side of each quail. Cook for 2 more minutes at 400 degrees F until the glaze is caramelized and the internal temperature of the thickest part of the thigh reads 165 degrees F.
Transfer the quail to a serving platter and let them rest for 3 minutes. Drizzle any remaining glaze over the top and serve with lemon wedges alongside.