Fill a large 24-quart pot with 8 quarts of water and bring it to a boil over high heat. Add the seafood-boil seasoning pouches, cayenne pepper, salt, onions, and celery.

Squeeze the juice from the lemon wedges into the pot and toss in the wedges. Add the garlic cloves, still in their skins, to the pot.

Cover the pot and let the water come to a rolling boil. While waiting, place the corn pieces in a single layer on a baking sheet and freeze them.

Once the water is boiling, taste it. The broth should be spicy and salty, and you may see a bright orange foam forming.

Add the potatoes and kielbasa. Allow the water to return to a boil, then turn off the heat. Let everything soak for about 10 minutes, until the potatoes are nearly tender when pierced with a knife.

Bring the pot back to a boil, and toss in the shrimp. Cook for 3 minutes, then turn off the heat again. Add the corn, and let everything soak for another 7 minutes.

Drain the mixture and serve immediately with your favorite dipping sauces or rémoulade.