In a Dutch oven or 3-quart saucepan, heat oil until shimmering. Stir in garlic and ginger until fragrant, about 1 minute.
Stir in broth, water, soy sauce, mirin, and sesame oil. Bring to boil, reduce heat to a simmer, and add dried mushrooms.
Simmer until mushrooms have softened, about 10 minutes.
Using two large shallow bowls, divide chicken and noodles. Top with hot broth and garnish with eggs, scallions, and chilis.
Thai bird chiles are similar to Serrano chilis but often smaller and spicier. You can find them at some well-stocked grocery stores or Asian grocery stores. They are just for garnish and heat, so if you can't find them, don't worry about it.