In a large Dutch oven or stock pot, bring the broth and garlic to a simmer over medium heat. Stir in the soy sauce, vinegar, and chili paste.
Add the mushrooms and reduce the heat to low. Simmer for 6 to 8 minutes.
Add the ramen noodles and turn the heat up to medium high.
Cook until the noodles are al dente (about 3 to 4 minutes), stirring while it cooks. Mix in the sesame oil and season with salt to taste.
Serve with green onion on top.