Peel and devein the shrimp, placing the shells in a large soup pot. Add the water to the pot, cover, and bring to a simmer over high heat. Uncover, reduce the heat to medium-low, and gently simmer for 1 hour. Strain the broth through a medium-mesh sieve into a bowl, pressing on the shells to release liquid. Discard the shells. Pour the broth back into the soup pot and bring to a simmer over medium heat.
Use a vegetable peeler to remove the rind from the lime in strips; reserve the lime. Add the lime strips to the pot. Smash the lemongrass pieces with a heavy pan or butt of a knife to release the essential oils. Add the lemongrass, ginger, and mushrooms to the pot, and simmer over medium heat for 10 minutes.
Stir in the chile paste and fish sauce; bring to a boil. Stir in the shrimp, scallions, cilantro, and noodles. Cook until the shrimp are bright pink and the noodles are tender, about 3 minutes.
4. Squeeze the juice from the reserved lime into the pot. Serve hot.
Tip: To peel fresh lemongrass, trim off the stem and dry green leaves and then pry away a few of the tubular outer layers until you are left with only a pale-white stalk 4 to 5 inches in length.
For even more flavor, top the soup with roasted peanuts and serve it with lime wedges for squeezing.