In a large pot add brown sugar, salt, bay leaves, coriander, ground peppercorn, mustard and 2 cups of water. Bring to a boil. Reduce heat to low and simmer until sugar and salt begin to dissolve, about 5–6 minutes. Pour brine into a large bowl. Add cold apple cider. Set aside to cool.
While brine cools, prepare the rib roast by removing the membrane that covers the rib bones, removing any excess fat from the outside, and frenching the tips of the ribs.
Place rib roast in large plastic bag along with brining liquid. Seal bag and refrigerate for 4–8 hours. One hour before you are ready to cook the roast, remove from refrigerator and let it come to room temperature.
Preheat oven to 250°F. Remove rib roast from brine and pat dry with paper towels. Place in a roasting pan or large baking dish, rib side down. Smother the top side of the roast with mustard.
Cover loosely with aluminum foil and place in oven for 1.5 hours. For the last 20–30 minutes of cooking, remove the aluminum foil and increase the heat to 375°F, as this will brown/crisp the outside of the roast.
Remove from oven and transfer rib roast to a cutting board; let rest 20 minutes before serving.