1 cup chicken stock or broth
¼ cup ketchup
1 tbsp. each light and dark soy sauce
2 tsp. cornstarch
1 tbsp. canola or olive oil, plus more if needed
4 oz. shiitake mushrooms, stemmed and sliced
1 small leek, white and light-green parts only, chopped
1 small rib celery, chopped
2 cups shredded green cabbage
2 cloves garlic, chopped
1 piece ginger (1 inch), peeled and minced or grated
White pepper, for seasoning
¾ to 1 lb. lump crabmeat or king-crab leg meat, picked over for shells
1 cup mung bean sprouts
10 to 12 large eggs
1 tbsp. light soy sauce, tamari, or shoyu
1 tbsp. toasted sesame oil
1 tsp. cornstarch
2 tbsp. hot sauce
Toasted sesame seeds and finely chopped chives or scallions, for serving
For the gravy, combine stock and ketchup in a small pot over medium-high heat. In a small bowl, stir together soy sauce and cornstarch until smooth, then add to stock. Bring sauce to a low boil over medium-high heat, whisking constantly, then reduce the heat to medium, simmering until thickened, about 2 minutes.
For the omelet, heat oil in a large nonstick skillet over medium-high heat. Add mushrooms and cook until browned, 6 minutes, stirring often. Add leek and celery, stirring, for 1 to 2 minutes, until starting to soften. Stir in cabbage, garlic, and ginger; season with salt and white pepper. Stir in crab and sprouts until combined. Remove half of the mixture to a plate.
Meanwhile, in a large bowl, whisk eggs. In a small bowl, whisk together soy sauce, sesame oil, cornstarch, and hot sauce. Stir mixture into the eggs.
Pour half of the egg mixture over the vegetables and crab in skillet, then cover and cook, still over medium-high, until bottom of omelet is browned and top is set, 3 to 4 minutes. Top pan with a plate or a cutting board and flip omelet out of pan; slice in half. Repeat with the remaining vegetables, crab, and eggs, adding more oil to the pan if necessary. Top each portion with gravy, sesame seeds, and chives or scallions.