Prepare the Broth: In a medium pot, sauté garlic and ginger in oil for 30 seconds. Add broth, soy sauce, chili oil, gochujang, sesame oil, brown sugar, and lime juice. Simmer 10 minutes.
Cook Dumplings: In a skillet, heat sesame oil. Add dumplings, brown 2–3 minutes per side, add water, cover, and steam for 4 minutes.
Cook Shrimp: In the same pan, heat olive oil, add seasoned shrimp, and sauté 2–3 minutes per side until pink.
Cook Noodles: In simmering broth, cook noodles for 3 minutes, stirring gently.
Assemble: Divide noodles and broth into bowls, top with shrimp, dumplings, eggs, scallions, chili, and extra chili oil.
