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1
Fill a very large stockpot with the water. Add the Old Bay, squeezed lemon halves, bay leaves, and cayenne. Bring to a rolling boil over high heat, then taste the water: it must seem almost uncomfortably salty, spicy, and lemony. The shells and skins of every component will buffer this seasoning; if the water is merely pleasant, add more Old Bay until it is not.
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2
Add the whole new potatoes to the boiling seasoned water. Maintain a steady boil and cook for 15–20 minutes, until a knife meets only slight resistance at the centre of the largest potato.
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3
Add the corn pieces to the pot. Continue boiling for 8–10 minutes, until the kernels are just tender when pressed with a fingernail.
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4
Add the sausage chunks. Boil for 5–7 minutes, until the cut faces have deepened in colour and the fat is rendering visibly into the water.
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5
Add the shrimp in a single mass. This is where the dish lives or dies: the shrimp are the clock for the entire pot, and the margin between perfectly cooked and rubbery is sixty seconds. Watch the shrimp constantly. The moment they are uniformly pink and curled into a tight C, pull the pot from the heat immediately — 3 to 5 minutes maximum.
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6
Drain the pot rapidly through a large colander. Speed is essential: residual heat continues cooking as the components sit. Dump the entire contents directly onto a newspaper-covered table in one motion. Serve with the Old Bay drawn butter, cocktail sauce, lemon wedges, and paper towels — no plates.