Combine lemongrass, garlic, chiles, ginger, and lime zest in a food processor. Process until a fine paste forms.
Place beef in a bowl and season with salt and pepper. Heat oil in a large Dutch oven over medium-high heat. Cook beef, turning occasionally, until browned, 10 to 15 minutes. Transfer beef to a plate.
Cook lemongrass paste in the same Dutch oven stirring often, until beginning to soften, 5 to 8 minutes. Add soy sauce, brown sugar, fish sauce, browned beef and any juices, and 10 cups water. Bring to a boil and reduce heat. Simmer stew, partially covered and skimming occasionally, until beef is tender and liquid is slightly thickened, 2 1/2 to 3 hours.
Meanwhile, preheat the oven to 350 degrees F (175 degrees C). Place coconut flakes on a rimmed baking sheet.
Toast coconut in the preheated oven, tossing occasionally, until golden around the edges, about 4 minutes. Set aside.
Add carrots and shallots to the stew. Continue cooking, partially covered, until vegetables are soft and beef is falling apart, 35 to 45 minutes more. Stir in green onions.
Bring a large pot of lightly salted water to a boil. Cook rice noodles in boiling water, stirring occasionally, until noodles are tender yet firm to the bite, 5 to 7 minutes, or according to package directions.
Divide cooked noodles into individual bowls and ladle stew on top. Top with toasted coconut and serve with lime wedges.
