Make the brine: Remove 3 wide strips zest from the orange with a vegetable peeler. Squeeze 3 tablespoons orange juice and set aside. Combine 2 strips of the zest, 4 cups water, 1/3 cup salt, 1/2 cup brown sugar, the star anise, pickling spice and ginger slices in a medium saucepan over medium-high heat. Cook, stirring frequently, until the salt and sugar dissolve. Remove from the heat and add 4 cups cold water; let cool to room temperature.
Put the ribs meat-side down on a cutting board. Insert a paring knife between the membrane and the bones on one end, then loosen the membrane with your fingers and gently pull it off. Put the ribs in a roasting pan and pour the brine on top. Cover and refrigerate overnight.
Meanwhile, make the sauce: Heat the vegetable oil in a small saucepan over medium heat. Add the garlic and grated ginger; cook 1 minute. Add the sherry, bring to a boil and cook until slightly reduced, 1 to 2 minutes. Stir in the remaining 1/4 cup brown sugar, the 3 tablespoons orange juice, the remaining 1 strip orange zest, the chicken broth, vinegar and soy sauce and simmer until reduced to about 1 cup, 8 to 10 minutes. Remove from the heat and let cool. Set aside 1/4 cup sauce for serving; use the rest for brushing. (The sauce can be made up to 1 day in advance.)
Prepare a grill for indirect heat: For gas, preheat to medium high, then turn off half of the burners and turn the other burners to medium low. For charcoal, once the coals ash over, push them to one side.
Remove the ribs from the brine and pat dry. Mix 1 1/2 teaspoons black pepper and the cayenne in a bowl and rub on the ribs. Put bone-side down on the cooler part of the grill; cover and cook 1 hour. Brush with 1/2 cup of the sauce; cover and cook 1 more hour, brushing with more sauce during the last 10 minutes. Transfer to a cutting board and slice into ribs. Serve with the reserved sauce.