Prepare the Chicken
1. Pat the chicken leg quarters dry with paper towels, then place them in a large bowl. Drizzle with 1 tablespoon of olive oil and sprinkle the paprika, garlic powder, onion powder, black pepper, salt, and chili flakes evenly over all pieces. Toss well to coat every surface.
2. Allow the seasoned chicken to sit at room temperature for 10 to 15 minutes, letting the flavors penetrate the meat before grilling.
3. Heat your grill to medium-high heat, about 400 to 425 degrees Fahrenheit, ensuring the grates are clean and lightly oiled to prevent sticking.
Prepare the Potatoes and Coleslaw
1. Cut each potato lengthwise into wedges about 1 to 1.5 inches thick, then toss them in a bowl with the 2 tablespoons of oil, salt, and black pepper, stirring to coat evenly.
2. Place the potatoes directly on the grill grates in a single layer and cook for 15 to 20 minutes, stirring occasionally, until golden brown and crispy on the outside with tender interiors, or spread on a baking sheet and roast at 425 degrees Fahrenheit for 20 to 25 minutes.
3. In a small bowl, whisk together the mayonnaise, plain yogurt, and lemon juice until smooth and well combined.
4. Place the coleslaw mix and sliced cucumber in a large bowl, then pour the dressing over and toss until every piece is lightly coated.
Grill the Chicken
1. Carefully lay the seasoned chicken pieces skin-side down on the preheated grill, spacing them so they don't touch, and let them cook undisturbed for 8 to 10 minutes to develop a flavorful crust.
2. Flip the chicken pieces and cook on the other side for another 10 to 12 minutes, until the skin is charred and crispy and the meat is cooked through (internal temperature of 165 degrees Fahrenheit at the thickest part).
3. Transfer the cooked chicken to a clean plate and let it rest for 5 minutes before plating, allowing the juices to redistribute.
Assemble the Plate
1. Divide the crispy potato wedges evenly among four plates, arranging them in a cluster in the center or off to one side.
2. Place one chicken leg quarter on each plate, positioning it so the smoky, crispy skin is visible and appetizing.
3. Spoon a generous portion of the cool coleslaw beside the chicken and potatoes, creating a nice contrast between hot and cold elements.
4. If desired, scatter fresh herbs over the top and add lemon wedges on the side for a burst of brightness when guests squeeze them over their meal.