Simmer the napa cabbage leaves for about 1 minute until softened.
Cook finely diced eggplant in a pan with a little oil for 8-10 minutes until soft and lightly golden. Transfer to a plate.
In the same pan, cook the mushrooms until all excess moisture evaporates and they start to brown. Add garlic, ginger, and green onions. Cook for 1 more minute.
Add the eggplant back in along with the soy sauce, maple syrup, and rice vinegar. Cook for another 1-2 minutes, then fold in the rice.
Fill each cabbage leaf, fold in the sides, and roll tightly.
Pan-sear the rolls seam-side down until golden on multiple sides.
For the sauce, simmer broth, soy sauce, maple syrup, rice vinegar, sesame oil, and dried ginger for 1-2 minutes. Stir in the cornstarch mixed with water and cook until glossy.
Pour the sauce over the cabbage rolls and top with green onions and sesame seeds.
