Heat coconut oil in a large pot. Add shallot and white scallion parts; cook until golden and fragrant.
Stir in mushrooms and cook until softened. Add shrimp and cook until pink.
Add ginger, garlic, and chili paste; cook until fragrant.
Stir in soy sauce, rice vinegar, and vegetable broth. Bring to a boil, then simmer for 10 minutes.
Mix cornstarch with water, add to broth, and simmer for 8–10 minutes until glossy.
Turn off heat, slowly drizzle in beaten egg while stirring.
Season with salt and pepper; garnish with sesame oil, scallions, and red pepper flakes.
