Pat the shrimp dry with a paper towel and season evenly on both sides with 1 teaspoon salt and black pepper.
Heat the oil in a medium (10-inch) Dutch oven over medium-high heat. Working in batches to avoid overcrowding, add the seasoned shrimp and cook, undisturbed for 2 minutes until lightly browned. Flip and cook for 2 minutes more. Transfer to a plate and set aside. Repeat with the remaining shrimp.
Add the scallion whites, garlic, and ginger. Cook, stirring, until the aromatics are softened and fragrant, 1 to 2 minutes. Add the lime juice and stir, scraping up any browned bits from the bottom of the pot.
Increase the heat to high and add the Lemongrass Broth, seafood stock, coconut milk, soy sauce, the remaining ½ teaspoon of salt, and fish sauce. Bring the mixture to a boil, about 4 minutes. Add the noodles and cook, stirring often, until al dente, according to package directions.
Turn off the heat. Add the cooked shrimp, carrots, and cilantro and toss to combine. Taste and adjust the seasoning as needed. Divide among bowls and garnish with additional cilantro.
