Bring 1 gallon of water to a boil in a large pot, then add the bruised lemongrass stalks, halved garlic heads, sliced ginger, fish sauce, salt, Old Bay seasoning, star anise, and lemon wedges. Reduce heat to medium-low and simmer for 15 minutes to extract deep, layered flavors from the aromatics. I like using head-on shrimp because the heads will infuse the broth with even more umami, so don't skip this if you can find them.

Add the halved potatoes to the simmering broth and cook for 12-15 minutes until they're just tender but still hold their shape. Add the corn pieces and cook for 2 more minutes to gently soften them. Then add the shrimp and sliced andouille sausage, cooking for just 1-2 minutes until the shrimp begin to turn pink and curl slightly. The shrimp will continue cooking from residual heat, so don't overcook them at this stage.

Drain the shrimp, sausage, potatoes, and corn in a colander, discarding the broth along with the now-spent lemongrass, garlic, ginger, and lemon wedges. Set the drained ingredients aside in a large serving bowl or shallow platter. I recommend reserving about 1/4 cup of the broth before draining—you can add it to the butter sauce if you want a slightly looser consistency for dipping.

In a medium saucepan over medium-low heat, melt the unsalted butter, then add the finely minced garlic and minced lemongrass. Cook gently for about 2 minutes, stirring frequently to infuse the butter with these aromatics without browning the garlic. Remove from heat and stir in the paprika, cayenne, black pepper, sugar, lemon juice, and Louisiana hot sauce or Sriracha until fully combined and smooth. Finish by stirring in the julienned kaffir lime leaves, lime juice, and salt, tasting and adjusting seasoning as needed.

Pour the warm aromatic butter sauce over the drained shrimp, sausage, potatoes, and corn, then gently toss everything together until evenly coated. Transfer to a serving platter and serve immediately while still warm, with extra sauce on the side for dipping if desired.