Preheat oven to 375 degrees F.
Dry the skin of the turkey breasts with paper towels and put in a roasting pan on a wire rack, breast side up. Rub 4 tablespoons butter all over the surface of each breast and season them well with salt and pepper. Add the shallots to the bottom of roasting pan and cover shallots with the stock. Transfer the pan to the oven and roast until an instant-read thermometer registers 165 degrees F and the juices run clear, about 1 hour. (Begin checking the internal temperature after 45 minutes to prevent overcooking.) Remove the turkey breasts from the oven to a cutting board and tent with foil. Allow to rest while making the gravy.
Strain pan drippings into a small pot over low heat and bring to a simmer. In a small bowl mash together the remaining 2 tablespoons butter and flour with a fork, until a paste forms. Whisk into the simmering stock, season with salt and pepper, to taste, and cook until thickened.
Carve the turkey breast meat from the bone and arrange the slices on a serving platter. Serve with gravy on the side.