Step 1: Pat the chicken thighs dry. In a medium bowl, combine 2 tbsp olive oil, 1 tbsp lemon juice, 2 minced garlic cloves, dried oregano, 1/2 tsp salt, and 1/4 tsp black pepper. Add chicken, toss to coat, and refrigerate for 30 minutes to 4 hours.
Step 2: Preheat your grill to medium-high heat (about 400°F/200°C). Lightly oil the grill grates.
Step 3: For the herbed yogurt sauce: In a small bowl, combine Greek yogurt, 1/4 cup fresh dill, 2 tbsp fresh parsley, 1 minced garlic clove, 1 tbsp lemon juice, 1 tsp olive oil, and salt and pepper to taste. Stir well, cover, and refrigerate.
Step 4: Wash and quarter the potatoes. Place in a large pot of salted water and bring to a boil. Cook for 8-10 minutes until just tender, then drain thoroughly.
Step 5: Preheat oven to 425°F (220°C). On a baking sheet, toss par-boiled potatoes with 2 tbsp olive oil, 1/4 cup chopped fresh dill, garlic powder, 1/2 tsp salt, and 1/4 tsp black pepper. Spread in a single layer.
Step 6: Roast potatoes for 25-35 minutes, flipping halfway, until golden brown and crispy.
Step 7: Place marinated chicken thighs on the preheated grill. Grill for 5-7 minutes per side, or until internal temperature reaches 165°F (74°C) and chicken is cooked through with nice grill marks.
Step 8: Remove chicken from grill and let rest for 5 minutes.
Step 9: Arrange grilled chicken and crispy dill potatoes on plates. Drizzle generously with the herbed yogurt sauce and garnish with extra dill or parsley. Serve immediately.