Preheat oven to 400°F. If you are working with freestone peaches, cut in half lengthwise. If your peaches are clingstone, cut as best you can into nice large wedges. Put cut pieces into a baking dish, cut sides up. Sprinkle the peaches with the sugar, then pour the vinegar and wine over. Add the bay leaf to the liquid. Roast peaches in the oven until the fruit is tender, about 20 minutes.
Cut the feta into four squares, then place in individual bowls.
Place the peach halves or pieces around the feta. Spoon some of the roasting juices over the peach pieces and feta. Drizzle olive oil over the top. Sprinkle with black pepper and Urfa biber and serve.