Position 2 racks in the upper and lower thirds of the oven and preheat to 400 degrees F. Cut four 16-inch long sheets of parchment paper. Fold each sheet in half and open like a book. Divide the pieces of parchment between 2 baking sheets (2 pieces per sheet).
Place the noodles in a large bowl and cover completely with warm water. Let sit for 5 minutes to soften, then drain well. Dry the bowl and put the noodles back in, along with the spinach and carrot: reserve.
Whisk the coconut milk, curry paste, fish sauce, garlic, lime zest and juice, and brown sugar together in a medium bowl. Add 1/4 cup of the coconut marinade to the noodles, season with 1/8 teaspoon salt and toss to coat. Add the shrimp to the remaining marinade and toss to coat.
Divide the noodles and vegetables between the 4 sheets of parchment, placing on one side of the fold. Drizzle each serving with 2 tablespoons water. Top with shrimp and drizzle with remaining marinade. Cut each lemongrass stalk into 4 pieces and smash with mallet or other heavy item. Place 2 in each pack.
Fold over the top half of the parchment, crimping and overlapping small folds along the open edge to seal tightly. Bake until the parchment puffs, about 12 minutes; the shrimp will be cooked through.
Transfer each pack to a plate. Avoiding the hot steam, carefully cut open each pack and discard the lemongrass stalks. Serve with lime wedges.