Cover the dried mushrooms, wood ear, lily flowers, bean curd sticks, and vermicelli separately in cold water for 30-40 minutes. Drain, squeeze dry, slice mushrooms, trim wood ear, and cut bean curd sticks into 5-6 cm lengths. Strain and reserve the mushroom soaking water for the braise.
In a small bowl, mash the nam yu cubes with their liquid into a smooth paste, loosening with a spoonful of reserved mushroom water.
Heat oil in a wok over medium heat and stir the ginger until fragrant. Add the mashed nam yu and stir-fry 30 seconds until glossy and deeply savory.
Add the soaked mushrooms, wood ear, carrot, and chopped cabbage. Stir-fry 2-3 minutes to coat, then season with the soy sauce.
Pour in about 2 cups of strained mushroom soaking liquid, top up with water if needed to nearly cover. Add rock sugar, bring to a gentle simmer, cover, and braise 8-10 minutes until tender and glossy.
Add the soaked bean curd sticks and vermicelli, submerging them in the gravy. Cook 2-3 minutes until springy and the sauce thickens. Drizzle with sesame oil, toss once, and serve hot over rice.