Remove the zest from the oranges in wide strips using a vegetable peeler, applying only gentle pressure so that most of the white pith is left behind. Reserve the zest, juice the oranges and strain the juice into a small saucepan. Add the zest, salt, bourbon, sugar, peppercorns, tea bags, cloves, bay leaves and 1 quart (4 cups) of water. Bring to a boil, then turn off the heat and let the mixture sit for 30 minutes. Pour the brine into a plastic container or pot large enough to hold the turkey, add 5 quarts (20 cups) ice water and stir to combine. Submerge the turkey, adding more ice water if needed. Weight it down with a plate to keep it submerged and refrigerate at least 8 hours and up to 12 hours.
Drain, rinse and pat the turkey dry. Place on a large paper-towel-lined cutting board and let sit out at room temperature until it reaches room temperature, about 1 hour.
For the honey-mustard butter:
Mix the butter, Dijon, spicy brown mustard and honey in a medium bowl until well combined.
Position a rack in the middle of the oven and preheat the oven to 375 degrees F.
Pat the turkey skin dry again and rub the honey-mustard butter evenly over the surface, also pushing some underneath the skin of the breasts. Lay the turkey in a large roasting pan as flat as possible. If the pan is a bit small, tuck the wings behind the back with the drumsticks resting on the ledge of the pan and place a large rimmed baking sheet lined with aluminum foil at the bottom of the oven to catch drippings.
Roast, basting the turkey with the pan drippings every 30 minutes or so, until a meat thermometer inserted in the thigh registers 165 degrees F, 1 hour 30 minutes to 2 hours. Transfer to a cutting board and let rest 30 minutes before serving.
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