Using scissors or a small, sharp knife, cut through the shell along the rounded back of each shrimp; remove the vein. In a large pot, stir 4 quarts water, the beer and the Old Bay; season with salt. Add the onions and the halved garlic head. Squeeze in the juice from the 2 halved lemons, then add the lemon halves; bring to a rolling boil.
Meanwhile, in a food processor, puree the butter, parsley and garlic clove to form a smooth paste. Transfer to a saucepan and heat over medium until the butter melts; season. Cover and keep warm.
Add the potatoes to the large pot; cook until almost tender, about 12 minutes. Add the corn and cook until tender, about 5 minutes. Remove from the heat; add the shrimp and let stand, stirring occasionally, until the shrimp are just opaque in the center, about 3 minutes.
Using a large slotted spoon, transfer the shrimp, potatoes, corn and garlic to a large platter (discard the onions and lemons); drizzle with the parsley butter. Serve with the lemon wedges and more Old Bay for sprinkling.