Preheat the oven to 375 degrees F.
After the turkey has brined, remove the turkey roast from the brine and pat dry with paper towels. Discard the brine.
Place the turkey roast on a cutting board skin side down. Open the turkey roast to expose the center of the roast. Add 1 tablespoon of butter to the middle of the roast then carefully roll it back up into a roll with the skin side facing out.
Carefully use your fingers to lift the turkey skin away from the meat, creating a pocket, making sure to not tear the skin. Next, take 1 tablespoon of the honey-thyme butter and place it in the pocket between the skin and the meat. Fold the skin over the butter and press the butter down to spread it across the breast meat below the skin. Repeat on the other side of the turkey breast roast.
Use butchers twine to tie the turkey roast up so that it holds its shape while it cooks. I tie it about 4-5 times with the twine spaced out every inch along the turkey roast.
Spread the remaining honey-thyme butter on the outside of the turkey roast. This will make the turkey golden brown once cooked.
Place the turkey breast roast into a large baking tin along with the potatoes, carrots, shallots, chicken broth and white wine. Season the vegetables and turkey with salt and pepper. Bake uncovered for 1 hour and 20 minutes, making sure to baste the turkey every 20 minutes. If the turkey is getting too brown in the oven, cover it loosely with aluminum foil.
Remove the turkey from the oven once a digital thermometer inserted into the center of the turkey roast reaches 160 degrees F. Remove the turkey from the pan, place on a cutting board, and cover with aluminum foil. Allow the turkey to sit for 20 minutes. This will help the juices redistribute in the turkey and will continue cooking due to the heat. The turkey will be fully cooked once it reaches 165 degrees F.