Whisk Greek yogurt, oil, lemon juice and zest, garlic, salt, paprika, cumin, oregano, onion powder, black pepper and optional cayenne until uniform.
Do not rinse the raw chicken. Open each thigh flat and place it directly in a food-safe bag or nonreactive container.
Add marinade and turn every piece until all surfaces have a thin even coating. Seal or cover and set on a rimmed plate.
Marinate in the refrigerator for at least 2 hours and up to 24 hours for the best flavor and texture.
Lift out the thighs and let loose marinade drip away. Scrape off thick clumps, leaving a thin film. Discard the used marinade and bag.
Grill at 425°F to 450°F for 9 to 14 minutes, roast on a rack at 425°F for 18 to 24 minutes, or air fry at 380°F for 12 to 15 minutes, turning once as appropriate.
Measure the thickest part of more than one thigh and continue cooking until every checked piece reaches at least 165°F.
Transfer with clean tongs to a clean platter, rest 5 minutes, then garnish with parsley and serve with fresh lemon wedges.