Khao Soi

Pulse shallots in a food processor until finely chopped, about 10 pulses. Transfer shallots to a bowl, and set aside. Pulse garlic in food processor until finely chopped, about 6 pulses. Transfer to a separate bowl, and set aside. Pulse radish and lemongrass in food processor until finely chopped, about 10 pulses. Transfer to a separate bowl, and set aside.

Heat oil in a medium Dutch oven over medium-high. Add onion and reserved shallots; cook, stirring constantly, until fragrant, about 30 seconds. Add reserved garlic; cook, stirring often, until onion and shallots are translucent, about 3 minutes. Add tomatoes and reserved radish-lemongrass mixture; cook, stirring often, until fragrant and tomatoes begin to soften, about 2 minutes. Add ground pork; cook, stirring constantly, until pork is broken into small pieces, about 1 minute. Add 2 tablespoons of the water. Reduce heat to low; cook, stirring often, until pork is no longer pink, about 15 minutes. Add soybean paste, red pepper powder, paprika, palm sugar, granulated sugar, black pepper, and 1 1/2 tablespoons of the fish sauce, stirring until evenly combined. Increase heat to medium; cook, stirring often, until slightly thickened, about 10 minutes. Reduce heat to low; cook, stirring occasionally, until thickened, about 10 minutes. Turn off heat; stir in grated galangal. Cover pork sauce, and keep warm using residual heat from burner.

During final 10 minutes of pork sauce cooking, bring remaining 12 cups water in a large saucepan to a boil over medium-high. Reduce heat to medium; add  rice noodles, stirring once, until softened, 30 to 40 seconds for fresh noodles or 2 to 3 minutes for dried noodles. (If using dried noodles, soak in warm water for 10 minutes before boiling noodles.) Transfer noodles to a colander using a slotted spoon, and drain well; reserve cooking water in saucepan. Place noodles in a large bowl; cover with cold water, and set aside. Add reserved shallot, garlic, radish, lemongrass, and onion peelings and trimmings to cooking water in saucepan; add salt and remaining 3 tablespoons fish sauce. Bring to a simmer over medium; simmer, stirring occasionally, 20 minutes. Pour broth through a fine mesh strainer into a large bowl, discarding solids.

Drain reserved noodles. Divide noodles evenly among 6 bowls (about 1 1/3 cups each). Top evenly with pork sauce (about 3/4 cup each), and add about 1 2/3 cups broth to each bowl; garnish with mint, cilantro, green onion, and mushrooms.