In a large stock pot, at least 20 quarts, add all the ingredients for the cooking liquid and enough water to fill the pot half way up.
Bring the pot to a boil over high heat, then add the baby potatoes and corn. Let them cook for 10 minutes.
Now begin adding the sausage and crab legs, cook for 10 minutes.
Add the lobster, let it cook for 3 minutes, then add the shrimp and cook for another three minutes until the shrimp are pink and opaque.
Drain the cooking liquid from the pot, pour the seafood boil over a serving tray or table lined with many layers of newspaper, and pour the seafood boil sauce over all the shellfish and vegetables.
Serve with the crab butter dipping sauce in a small bowl.
To Make the Garlic Butter Seafood Boil Sauce
While the seafood is boiling, melt the two sticks of butter with the garlic paste, brown sugar, Old Bay, smoked paprika, and lemon zest. Let cook for three minutes over medium heat, stirring occasionally so the garlic doesn't burn.
Whisk in the chicken stock and hot sauce and bring to a boil over medium-high heat. Then reduce the heat, and simmer for 10 minutes.
Take the pan off the heat, stir in the lemon juice and parsley, then set aside until the seafood boil is done cooking.
Make the Garlic Butter Dipping Sauce
In a medium sized saucepan, melt one tablespoon of butter over medium heat with the wine, grated shallots, grated garlic, fresh thyme, and lemon zest. Sauté for 1 to 2 minutes, it should be very fragrant.
Whisk in the chicken broth and lemon juice, let the mixture reduce down until there's about 3 tablespoons of liquid remaining.
Add the cream and turn the heat up to medium-high. Bring to a boil, then turn the heat down to low.
Whisking constantly, add the rest of the cold butter ONE tablespoon at a time, whisking until each one is incorporated completely before adding the next one.
Continue adding in all the butter, by the time the last tablespoon is done the sauce should be creamy and coat the back of a spoon.
Let sit at low heat, stirring occasionally, until ready to serve with the seafood boil.