1. Bring water to a boil. Add all ingredients for the brine and infuse for 5 minutes. Cool to room temperature and transfer to refrigerator until fully chilled.
2. Place the chicken into a large bowl or container and pour brine over until completely submerged. Brine in the refrigerator for 2 days.
3. Remove the chicken from the brine and dry very well with paper towels, inside and out. The less it steams, the drier the heat, the better.
4. Preheat the oven to 450°F
5. Truss the bird. Trussing is not difficult, and if you roast chicken often, it's a good technique to feel comfortable with. When you truss a bird, the wings and legs stay close to the body; the ends of the drumsticks cover the top of the breast and keep it from drying out. Trussing helps the chicken to cook evenly, and it also makes for a more beautiful roasted bird.
6. Place the chicken in a sauté pan or roasting pan and, when the oven is up to temperature, put the chicken in the oven. I leave it alone—I don't baste it, I don't add butter; you can if you wish, but I feel this creates steam, which I don't want. Roast it until it's done (internal temp approximately 165F), 50 to 60 minutes. Remove it from the oven and add the thyme, if using, to the pan. Baste the chicken with the juices (should be clear and not pink) and thyme and let it rest for 15 minutes on a cutting board.
7. Remove the twine. Separate the middle wing joint and eat that immediately! Remove the legs and thighs. I like to take off the backbone and eat one of the oysters, the two succulent morsels of meat embedded here, and give the other to the person I'm cooking with. But I take the chicken butt for myself. These are the cook's rewards. Cut the breast down the middle and serve it on the bone, with one wing joint still attached to each. The preparation is not meant to be super elegant. Slather the meat with fresh butter.
For the Mushroom Cream:
1. Sweat the shallots and porcini mushrooms in the butter.
2. Deglaze with sherry wine until all of the liquid is absorbed and nearly dry.
3. Cover with cream and add thyme.
4. Simmer for 30 minutes. Cover and infuse for 10 minutes.
5. Transfer to a blender and blend until smooth. Strain through a fine sieve.
For the Charred Carrots:
1. Do not peel the carrots but rather wash and scrub very well.
2. Dry off carrots, rub with coconut oil, place on a sheet pan and broil until charred and soft.
3. Season with salt to taste.