Step 1: Set up your grill for indirect grilling and preheat to medium-high (400 degrees).
Step 2: Meanwhile, make the Absinthe Herb Butter: Melt the butter in a heavy saucepan over medium-high heat. Add the garlic and cook until golden brown, 2 minutes. Add the herbs and cook for 30 seconds. Stir in the absinthe and cook for 1 minute. Remove the butter from the heat and let cool slightly.
Step 3: Either split the crab legs or remove a rectangle of shell from each leg to provide access to the meat. Arrange the crab legs on the grill grate, cut side up. Brush the crab with Absinthe Herb Butter. Indirect grill the crab until hot and lightly smoke flavored, 15 to 20 minutes, basting with the butter once or twice more. While you’re at it, grill the lemon halves directly over the fire until browned.
Step 4: Brush the crab once more with Absinthe Herb Butter. Serve with the lemon halves and any remaining butter in small bowls on the side for dipping.
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Steven Raichlen’s Project Smoke is a production of Maryland Public Television, Barbacoa, Inc., and Resolution Pictures. © 2017 Barbacoa, Inc.