Prep your vegetables. Peel the potato and using either a mandoline or a sharp knife, cut them into thin circles. Peel and jullienne your carrots.
In a large pot, over low/medium, heat the olive oil, garlic, and ginger. Let it cook for 2 minutes.
Whisk in the vegetable broth and coconut milk. Bring it to a simmer.
Add the peanut butter and gochujang. Whisk it until the peanut butter dissolves gracefully into the broth.
Add the lime juice, soy sauce, sliced potatoes, jullienned carrots, salt, and pepper. Bring the broth to a boil.
Reduce it to a simmer and let it cook for an additional 20-25 minutes.
While the broth is simmering, cook your somen in a separate pot according to the directions on the package.
After the broth is done simmering, take it off the heat and stir in the parsley and black sesame seeds.
Ladle your broth into a dinner bowl or something similar. Add your noodles on top. Garnish with additional parsley and black sesame seeds if desired. Eat it by dipping your noodles into the broth as opposed to eating it like a soup with a spoon!