Start by preparing all your ingredients since foil packet cooking moves quickly once assembled. Halve or quarter the baby red potatoes into 1-inch chunks, then boil them in salted water for 10 minutes until they're just starting to become tender but still firm enough to hold their shape—this ensures they'll cook perfectly in the packets without becoming mushy. While the potatoes cook, shuck the corn and cut it into 1-inch rounds, slice the andouille sausage into 1/2-inch thick pieces, mince the garlic fresh (I find fresh garlic gives a much more vibrant aroma than pre-minced), and juice the lemon. If using frozen shrimp, thaw them completely and pat dry with paper towels to remove excess moisture. Drain the potatoes well when done.
In a small bowl, combine the Old Bay seasoning, smoked paprika, salt, and pepper to create your seasoning blend. In a large bowl, toss together the thawed shrimp, sliced andouille sausage, parcooked potatoes from Step 1, corn from Step 1, minced garlic, lemon juice, and 3 tablespoons of melted and cooled butter. Sprinkle the seasoning mixture over everything and gently toss until all components are evenly coated. The key is to distribute the seasonings and butter uniformly so each packet has balanced flavor.
Tear off four large sheets of heavy-duty aluminum foil (about 15x18 inches each). Divide the seasoned mixture evenly among the four sheets, placing it in the center of each sheet. Fold each foil sheet in half over the mixture, then crimp and seal all three open edges tightly by folding them over multiple times—you want a secure seal so steam stays trapped inside. I like to crimp the edges firmly because loose packets let steam escape and you'll miss the beautiful braising effect. Make sure the packets are sealed well but not so tight that they're difficult to open safely later.
Preheat your oven to 400°F. Place the sealed foil packets on a large baking sheet and bake for 15-20 minutes until the shrimp are pink and cooked through and the potatoes are tender when pierced with a fork. If grilling instead, place packets directly on a grill rack over medium-high heat, grill for 8-10 minutes, carefully flip with tongs, then grill another 5-6 minutes. The packets will puff up slightly as they cook due to steam buildup—this is exactly what you want.
While the packets are cooking, melt 3 tablespoons of butter (I use Kerrygold salted butter for a richer, more complex sauce) in a small saucepan over medium heat. Let it cook undisturbed for 3-4 minutes, swirling occasionally, until it turns a golden amber color with a nutty aroma—watch carefully so it doesn't burn. Once the butter is brown, remove it from heat immediately and set aside.
Carefully open each foil packet by peeling back the foil (watch out for the hot steam). Transfer the contents to serving bowls or plates, pouring the cooking liquid from the packets over the top as well. Drizzle each serving with the brown butter sauce from Step 5, then top with fresh parsley and a squeeze of lemon juice. Serve immediately while everything is hot.