Place the lemon and onion slices in a baking pan large enough to hold them in a single layer. Place the chicken on top and sprinkle with the oregano, 1/2 teaspoon salt and 1/2 teaspoon pepper. Drizzle 2 tablespoons olive oil over the chicken. Rub the chicken to coat evenly with seasonings. Place under broiler to lightly brown the chicken skin, 5 to 10 minutes.
Remove chicken from broiler and set oven temperature to 325 degrees F. Pour the stock and wine into the pan and cover tightly with foil. Braise chicken in the oven until internal temperature reaches 165 degrees F, 30 to 35 minutes. Allow chicken to rest in baking pan, uncovered, for 30 minutes.
Meanwhile, place a large saucepan over high heat. Add the milk and 3 cups water and bring to a boil. Slowly add the polenta, whisking constantly to prevent lumping. Reduce the heat to low and cook, whisking occasionally to prevent sticking, until polenta is done, approximately 45 minutes. Add the cheese, vinegar, 1/2 teaspoon salt and 1/2 teaspoon pepper.
Place a large saute pan over medium-high heat. Once the pan is preheated add remaining 2 tablespoons olive oil and the greens. Season lightly with some of the remaining 1/2 teaspoon salt and 1/2 teaspoon pepper. Toss with tongs, lowering heat if necessary to prevent burning, until wilted and tender, then check the seasoning and adjust to your taste.
Preheat the broiler. Remove chicken from roasting pan and place on an ovenproof sheet pan. Remove and discard the onions and lemons. Pour the liquid from the roasting pan into a small saucepan and cook over medium-high heat until reduced to 1 cup. Place chicken in broiler and cook until skin becomes golden and very crispy, 5 to 10 minutes.
Spoon 3/4 cup polenta onto each of 4 to 6 large plates, then place 1/2 cup greens on top of each followed by a chicken leg. Spoon 2 tablespoons of the reduced chicken cooking liquid over the top of the chicken.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.