Make the dashi: In a small saucepan, combine kombu with 5 cups water and bring to a boil. Remove from the heat, discard kombu, and stir in bonito flakes. Let the dashi stand for 5 minutes, then pour through a fine sieve into a bowl and discard the bonito flakes. Let the dashi cool to room temperature and refrigerate for up to 3 days or until ready to use.
For the pork belly: Heat a 12-inch skillet over medium. Add the pork belly and 1 tablespoon water and cook, stirring, until the fat renders and the pork is golden brown, about 25 minutes. Using a slotted spoon, transfer the pork to a paper towel-lined plate and wipe the skillet clean.
In a medium bowl, toss the cooked pork with the miso, awamori, mirin, sugar, and 3 tablespoons water until evenly coated. Scrape the pork and sauce into the skillet, return it to medium heat, and cook, stirring, until the liquid reduces and the pork becomes sticky, about 10 minutes. Stir in the sesame seeds and remove the skillet from the heat. Meanwhile, heat the dashi in a small saucepan over low and keep warm.
Bring a medium saucepan of water to a boil. Add the mung beans and cook for 1 minute. Using a slotted spoon, remove the sprouts and transfer to paper towels to drain. Add the noodles to the boiling water and cook until tender, 2 to 3 minutes. Drain the noodles and divide them evenly among 6 serving bowls. Divide the dashi and mung beans among the bowls and top with the pork, scallions, and chile threads.