1. In a medium saucepan, heat the maple syrup. Add the garlic and cook over moderate heat for 3 minutes. Add the cinnamon and cayenne and cook for 1 minute. Add the cranberries and simmer for 5 minutes, then add the orange juice and simmer for 5 minutes longer. Transfer the hot mixture to a blender and puree. Pass the puree through a coarse strainer into a bowl and season with salt and pepper. Let the puree cool completely.
2. Loosen the turkey breast skin. Fold the wing tips under the breast to stabilize it. Put half of the spiced cranberry puree in a large resealable plastic bag and close. Cut off a corner of the bag and pipe the cranberry puree under the turkey breast skin; press the skin all over to evenly distribute the puree. Put the turkey breast on a plate, cover with plastic wrap and refrigerate overnight. Bring to room temperature before roasting.
3. Preheat the oven to 400°. Rub vegetable oil over the breast and season with salt and pepper. Stand the breast in a large roasting pan. Scatter the onion slices in the pan, pour in 2 cups of the turkey stock and roast for 30 minutes. Turn the oven down to 325° and add the remaining 4 cups of stock to the pan. Cover the breast with foil and roast for 1 1/2 hours longer.
4. Remove the turkey from the oven and discard the foil. Increase the oven temperature to 350°. Brush the breast with 1/4 cup of the remaining cranberry puree and roast for 20 minutes, or until glazed. Brush another 1/4 cup of the cranberry puree over the breast and roast for 15 minutes longer, or until the turkey is a deeply glazed crimson-brown and an instant-read thermometer inserted in the thickest part of the meat registers 145°. Transfer the turkey breast to a carving board and let rest for at least 15 minutes.
5. Strain the juices from the roasting pan through a coarse strainer set over a bowl; press on the onion to extract as much liquid as possible. Set a fine strainer over a medium saucepan and pour in the panjuices. Skim off the fat. Boil the juices until reduced to 3 1/2 cups, about 15 minutes. Stir in the remaining 1/2 cup of cranberry puree and season with salt and pepper. Pour this cranberry jus into a warmed gravy boat.
6. Cut down on either side of the breast bone and remove each turkey breast half in 1 piece. Thickly slice the breast halves crosswise and arrange on a platter. Pass the cranberry jus at the table.
Make Ahead: The cranberry puree can be refrigerated for up to 3 days.
Notes: One Serving With Skin: Calories 510 kcal, Total Fat 18.1 gm, Saturated Fat 5.2 gm