Preheat the oven to 300F/150C.

Prick duck skin all over with a sharp paring knife and season generously with salt and pepper. Place the legs in a Dutch oven and cook over medium-low heat until the duck is lightly browned and has rendered most of its fat, about 15 to 20 minutes. Turn once to color on both sides. Remove the legs to a bowl and drain off all but one tablespoon of the duck fat.

Add the olive oil to the same pot and, over medium-low heat, cook the onion, carrots, garlic and celery, stirring occasionally, until softened, 8–10 minutes. Place the duck back in the Dutch oven. Pour in the wine, and add the bay leaves, juniper berries, and peppercorns. Cover and bring to a boil.

Transfer the pot to the oven and braise the duck for about 2 to 2 ½ hours, until the bones are loosened from the meat. An hour before removing from the oven, gently stir in the vinegar.

About a half hour before the duck is done, make the bolenta: Bring milk and 2 cups water to a boil in a large saucepan. Season with salt and pepper; slowly stream in polenta, whisking constantly. Cook, whisking often, until it begins to thicken, about 5 minutes. Stir in the kefalotyri and butter. Continue whisking until the bolenta is smooth, thick and creamy. Cover and set aside.