Step 1: Run your fingers over the snapper fillets, feeling for bones. Pull out any you find with kitchen tweezers. Trim off any dark red portions from the skin side of the fillets using a sharp knife. (This is where the “fishy” flavor resides.)
Step 2: Place the honey, salt, peppercorns, cloves, allspice berries and water in a large deep bowl and whisk until the honey and salt are dissolved. Stir in the lemon zest. Add the fish, cover with plastic wrap, and brine in the refrigerator for 12 hours, turning several times. (Alternatively, place the fish and brine in a resealable heavy-duty plastic bag. Place the bag in a foil drip pan or baking dish to contain any leaks.)
Step 3: Drain the fish in a colander and discard the brine and lime zest. Rinse the snapper well under cold running water, drain, and blot dry with paper towels. Place on an oiled wire rack over a rimmed baking sheet. Let the snapper air-dry in the refrigerator until the surface is tacky, 2 hours.
Step 4: Set up your smoker following the manufacturer’s instructions and preheat to 275ºF. Add the wood as specified by the manufacturer.
Step 5: Smoke the fish on its wire rack until bronzed with smoke and cooked through, 30 to 45 minutes. To test for doneness, press it with your finger; the flesh should break into clean flakes. Alternatively, insert the probe of an instant-read thermometer through one end of the fish into the center. The internal temperature should be about 140ºF.
Step 6: Transfer the snapper on its rack to a rimmed baking sheet to cool to room temperature, then wrap in plastic wrap and refrigerate until serving. It will keep for at least 3 days in the refrigerator.
Use this in the Smoked Snapper Dip with Smoked Vegetable Chips recipe.