In a large bowl or glass pyrex dish, whisk together 2 tablespoons olive oil, 1 tablespoon lemon juice, and minced garlic. Add the chicken and season generously with dried oregano, smoked paprika, 1/2 teaspoon salt and 1/4 teaspoon pepper. Turn the chicken several times to coat with the marinade on all sides. Let the chicken marinate for a min of 30 minutes.
Heat the oven to 425° F. Place the diced potatoes and broccolini onto a parchment-lined sheet pan. Drizzle with 1 tablespoon olive oil and season with salt, pepper and dried oregano. Add the chicken drumsticks to the sheet pan and brush with the remaining marinade.
You may need 2 sheet pans so that the chicken, potatoes and broccolini are not crowded and have room to roast properly and not steam.
Roast for 40 minutes, flipping the potatoes once during roasting so they cook evenly and get caramelized and golden.
Plate the chicken, broccolini and potatoes onto a serving platter, top with remaining lemon juice, feta cheese crumbles and fresh dill.