Preheat the oven to 375°F and adjust a rack to the center.
In a small mixing bowl, combine the butter, 1 cup chopped oregano leaves, lemon zest, lemon juice, minced garlic, cinnamon, cumin, salt and pepper. Mix to blend. Set aside.
Add the onion slices, lemon slices, oregano sprigs, and the whole, sliced cloves of garlic to the bottom of an approximately 9 x 13 x 2-inch baking dish. Add about ½ teaspoon of the oregano butter to each onion.
Using your hands, loosen the skin of all the pieces of the chicken, except the wings. Evenly distribute about ⅔ of the remaining oregano butter among them, beneath the skin. Set aside.
Add the remaining butter to large sauté pan with a drizzle of olive oil, and place it over medium-high heat. Once it’s very hot, add the chicken, skin side down. (You should hear a sizzling sound — if you don’t wait until you do.) Let the chicken sauté just long enough to brown, about 2 minutes per side. Then, using kitchen tongs, remove the chicken pieces from the pan and place them directly on top of the onion slices in the baking dish.
Turn the heat to low under the sauté pan and add the stock and wine. Use wooden spatula to scrape the bottom of the pan, to work back in any bits of food that are stuck. Turn off the heat and pour this over the chicken. Cover the dish with foil and place it in the preheated 375°F oven. Braise until the chicken is almost all they way cooked, about 20 minutes. Then remove the foil and continue to cook just until the chicken is cooked through, 5 to 10 minutes.
Remove from the oven, sprinkle with a bit of salt and pepper and serve.