Preheat your oven to 400°F and fit a large, wire cooling rack securely inside a rimmed baking sheet, coating the rack generously with non-stick cooking spray. Pat the chicken pieces bone-in thighs and drumsticks completely dry on all sides using paper towels, which removes surface moisture so the coating can stick seamlessly.

In a wide, shallow bowl, vigorously whisk together the plain Greek yogurt and large eggs until completely smooth and unified. In a separate large bowl or a paper bag, combine the all-purpose flour, garlic powder, onion powder, smoked paprika, cayenne pepper, kosher salt, and black pepper, stirring firmly to distribute the spices evenly.

Submerge a dried piece of chicken entirely into the yogurt mixture, lifting it to let any heavy excess drip back into the bowl before dropping it straight into the seasoned flour mixture. Toss and press the flour firmly onto all sides of the chicken until it is entirely insulated in a thick, dry white coating, then shake off any loose powder.

Arrange the dredged chicken pieces skin-side up on the prepared wire rack, leaving at least a half-inch of space between each piece so the hot air can circulate uniformly. Stream the melted unsalted butter evenly across the floured tops of the chicken, which hydrates the flour starches and coaxes the crust into a deep golden color.

Bake uncovered at 400°F for 40 to 45 minutes without flipping. Watch for the exterior coating to turn a deep, shaggy golden brown and crisp up, checking that a meat thermometer inserted into the thickest part near the bone reads 165°F for the white meat or 175°F for the darker cuts. Remove from the oven and let the chicken rest flat on the wire rack for 5 minutes to lock in the internal juices before serving.