Add the olive oil to a soup pot over medium high heat.
Add the chopped shallots, garlic, ginger, and lemongrass. Sauté for 3-4 minutes, until fragrant.
Reduce heat to medium to add the gochujang, soy sauce, and vinegar. Stir for 1 minute.
Add the broth and lime juice. Stir to combine. Bring to a boil, then add the coconut milk and let simmer 10-15 minutes. Add chili crisp oil to taste.
Remove the aromatics with a slotted spoon.
Enjoy warm with crispy shiitake mushrooms, fresh cilantro, and noodles, if desired!