Preheat oven to 425° F. On a large baking sheet, toss the potatoes with 2 tablespoons olive oil. Season with salt and black pepper. Add the lemon halves. Roast for 20 minutes, or until tender. In a bowl, toss together 2 tablespoons olive oil, the chicken, dried oregano, paprika, shallot, salt, pepper, and chili flakes. Remove the potatoes from the oven and nestle the chicken around the potatoes. Arrange the onions, garlic, and lemon slices around the chicken. Add 1 slice of butter to each piece of chicken. Return the pan to the oven for 20-25 minutes more, until the chicken is cooked through.To make the dressing. Combine the remaining 1/3 cup olive oil, red wine vinegar, herbs, pepperoncinis, and olives.Remove the charred lemon slices and garlic cloves from the baking sheet. Finely chop the lemon slices, rind and all, discarding any seeds. Add half of the lemon to the dressing. Chop/mash the garlic into a paste, stir the garlic into the dressing. Season with red pepper and salt. Taste adding more of the lemon as desired.Break the feta over the chicken, then add the dressing. Top with fresh herbs. Eat and enjoy!