Drizzle the oil into a Dutch oven and heat over medium heat. Add the bacon lardons and saute until just browning on the edges, 3 to 4 minutes. Add the garlic and shallots and cook, stirring occasionally, until softened, another minute. Add the vermouth or white wine and bring to a boil. Add the chicken stock and then the mirin. Whisk in the dwenjang and gochujang until dissolved. Stir in the red chiles and then the mussels. Cover and shake occasionally to mix. Cook until the shells are all open, about 3 minutes. Discard any mussels that don't open.
Serve in large bowls to share and scatter chopped chives on top to garnish. Serve with lemon wedges and sticky rice on the side.