1. To Poach Garlic: Peel one whole head of garlic and purchase peeled garlic cloves. You should have about ¼ cup of garlic. Place the cloves in a small saucepan and cover them with a good quality olive oil. Place the pan over medium heat and heat to a simmer. Turn the heat down to a gentle simmer and poach the garlic for about ½ hour, or until it is golden brown and soft when pierced with a knife. Strain the garlic, reserving the oil for other uses. Mash the garlic with a fork and set aside.
2. For the Chicken: Adjust an oven rack to about 6-inches below the broiler element. Heat the broiler. Arrange the chicken halves skin-side down on a buttered or oiled baking sheet. Brush the chicken with a combination of olive oil and melted butter. Sprinkle with salt, pepper and Herbs de Provence. Broil until brown, about 8-10 minutes, basting once or twice. Turn chicken pieces over, season again and broil skin-side up until golden brown.
3. Sprinkle the grated Gruyere cheese over the chicken and return chicken to the oven. Change the oven setting to “bake” and adjust the temperature to 400 degrees. Pour about ¾ cup chicken broth into the pan and bake for 30 minutes, basting occasionally. If liquid evaporates, add stock and wine to pan drippings and continue basting. Roast until juices run clear, or for about 40 minutes. Remove chicken from the oven and transfer it to a platter to rest.
4. For the Pan Sauce: In a medium sauté pan, melt 2 tablespoons of butter. Add the shallots, season with salt and pepper and cook them over medium heat until they are soft and translucent. Meanwhile, pour off the fat from the bottom of the roasting pan and add some chicken stock or wine to help scrape up the pan juices and brown bits. Add the pan drippings to the sauté pan. Add the remaining chicken stock to the pan and thicken with the roasted garlic puree. Taste for seasoning. If using canned chicken stock, you may not need more salt. Butter can be added to enrich the sauce if you wish.