Bring 4 cups of water to a rolling boil in a large pot. Add the onion wedges, halved garlic bulbs, Old Bay seasoning, and thyme. Let this simmer for 2-3 minutes to allow the aromatics and spices to infuse into the water, creating a flavorful broth that will season everything that follows. This initial step is crucial because it extracts maximum flavor from the aromatics before the other ingredients go in.

Add the halved or quartered red potatoes to the seasoned boiling water along with a generous pinch of salt. Bring back to a boil and cook for 10-15 minutes until the potatoes are just tender when pierced with a fork but still hold their shape. Don't overcook them at this stage—they'll continue to soften slightly from residual heat. I find that cutting them into 1.5-inch pieces ensures they cook evenly without becoming mushy.

Stir in the corn pieces and sliced andouille sausage. Cook for about 6-7 minutes total—the corn will need about 3 minutes and the sausage will need about 4 minutes. The sausage is already cooked, so you're mainly heating it through and letting it infuse its smoky flavor into the broth, while the corn becomes tender-crisp.

Add the shrimp and cook for 1-2 minutes, just until they turn pink and opaque—this happens very quickly, so don't walk away. Immediately drain the entire pot through a colander to stop the cooking process. I prefer not to overcook shrimp because they become rubbery; that quick sear in the hot broth is all they need. Save about 1/2 cup of the cooking liquid to moisten the final dish if needed.

Transfer the drained shrimp boil to a large serving platter or individual bowls. Melt the butter with the lemon juice and drizzle generously over everything. Top with fresh parsley, black pepper, cayenne pepper, and a sprinkle of Old Bay. Serve immediately with crusty bread to soak up the buttery broth. The butter and lemon juice bring richness and brightness to balance all the smoky, seasoned flavors.