Bring pork and 6 cups water to a boil in a 4 qt saucepan over high heat. Cook until pork is tender (45 minutes). Transfer pork to an ice bath. Drain, dry completely, and discard skin. Cut pork into 1 inch pieces about 1/2 inch thick and set aside.
While cooking the pork belly, place chiles in a bowl and cover with 2 cups boiling water. Let sit until soft (15 minutes). Drain chiles, reserving 5 tbsp liquid.
Place chiles in a small food processor with dried shrimp, cilantro root, salt, garlic, shallots, lemongrass, ginger and galangal. Pulse until roughly chopped. Add reserved liquid and puree until smooth. Set 1/2 cup aside and refrigerate remaining paste for future use (up to 2 weeks).
Heat a 12 inch skillet or 13 inch wok over medium-high heat and add pork pieces. Cook, turning as needed, until browned on all sides and fat is rendered (12 minutes). Add garlic and cook until beginning to brown (1–2 minutes). Stir in the 1/2 cup curry paste.
Cook, stirring, until fragrant (1–2 minutes). Add fish sauce, peppercorns, palm sugar, lime leaves, chiles, ginger and 2/3 cup water. Bring to a boil. Add beans and cook, stirring occasionally, until tender (15 minutes). Remove from heat and stir in basil. Serve with jasmine rice on the side.