Step 1

Grate zest from 1 lemon to measure 2 teaspoons. Set grated zest aside. Cut zested lemon and remaining lemon into quarters; set aside. Melt butter in a small saucepan over low. Stir in Cajun seasoning, minced garlic, 1/8 teaspoon salt, hot sauce to taste, and reserved lemon zest. Remove from heat; cover to keep warm.

Step 2

Place a 24-quart pot on an outdoor propane burner. Add 11 quarts water, wine, clam juice, onion, garlic heads, bay leaves, thyme, quartered lemons, and remaining 5 tablespoons salt to pot; cover and bring to a boil over high flame. Stir in crab boil packets; cover and cook 10 minutes. Place a fitted strainer inside pot.

Step 3

Add potatoes to strainer in pot; cover and cook 5 minutes. Stir in corn and sausages; cover and cook until a thermometer inserted in thickest portion of sausage registers 155°F (or until heated through if using smoked sausages), about 10 minutes. Stir in shrimp; cook, uncovered, until shrimp are pink, opaque, and cooked through, 2 to 4 minutes.

Step 4

Lift strainer from pot, letting liquid strain back into pot, and transfer shrimp boil mixture (potatoes, corn, sausage, and shrimp) to a large heatproof bowl; discard onion, garlic, bay leaves, thyme, lemons, crab boil packets, and strained liquid inside pot. Add reserved butter mixture to shrimp boil mixture; toss to coat. (If you don't have a large enough bowl, you can do this step in batches, tossing half of the shrimp boil with half of the butter mixture at a time.) Arrange coated shrimp boil on a platter or a covered table. Season with additional Cajun seasoning or Old Bay, if desired. Serve with cocktail sauce and mustard, if desired.