Place pork belly into a pot and cover with water. Add ginger and Sichuan peppercorns. Bring to a simmer over medium-high heat; reduce heat to medium-low. Cover and cook until some of the fat has rendered out, about 20 minutes.
Remove the pork from the pot and cool to room temperature, about 15 minutes. Drain. Cut the pork into thin slices, about 1/8 inch thick. Return pork slices to pot. Stir in chile bean paste, sweet bean paste, and sugar. Cover and cook over medium heat until the pork is tender, 15 to 20 minutes.
Heat 1/2 teaspoon oil in a wok over medium heat. Cook and stir green bell pepper and salt until starting to soften, 3 to 5 minutes. Transfer to a dish.
Heat remaining 2 1/2 tablespoons oil in a wok over medium-high heat. Cook and stir pork until pieces begin to shrink and brown, 3 to 5 minutes. Return green bell pepper to the wok. Cook and stir until fragrant, about 2 minutes.