Step 1: Place the fruit in a nonreactive bowl. Add the 1/4 cup brown sugar, flour, lime zest, lime juice, and candied ginger. Stir to mix, adding sugar to taste. Spoon into the cast iron skillet.
Step 2: In the bowl of a food processor fitted with the metal blade, combine the butter, shortbread, nuts, brown sugar, cinnamon, and salt. Pulse until the mixture is coarse and crumbly. The butter should form pea-size pieces. Do not over-process, or the mixture will become gummy. Add the coconut and pulse for a few seconds just to mix. Spoon this mixture evenly over the fruit in the skillet.
Step 3: Set up the grill for indirect grilling and preheat to medium-high. If using a gas grill, place all of the wood chips or chunks in the smoker box or in a smoker pouch and run the grill on high until you see smoke, then reduce the heat to medium-high. If using a charcoal grill, preheat it to medium-high, then toss all of the wood chips or chunks on the coals.
Step 4: When ready to cook, place the skillet in the center of the hot grate away from the heat and cover the grill. Cook the crisp until the filling is bubbling and the topping is nicely browned, 40 to 60 minutes. Let the crisp cool for a few minutes. Serve with whipped cream or vanilla ice cream, if desired.
Serve with Smoked Ice Cream.