Bring a large pot of water to a boil. Carefully remove the core from the Napa cabbage and place the head in the boiling water for about 2-3 minutes until the leaves are pliable. Remove and cool.

Once cooled, gently peel off the leaves and set aside.

In a mixing bowl, combine cooked rice, chopped mushrooms, grated carrot, minced garlic, soy sauce, sesame oil, ginger, salt, and pepper. Mix well.

Take a cabbage leaf, place about 2-3 tablespoons of the filling at the base, fold in the sides, and roll tightly. Repeat with remaining leaves and filling.

In a skillet, combine vegetable broth, soy sauce, and sugar. Bring to a simmer. Add the cornstarch mixture and stir until thickened.

Preheat the oven to 375°F (190°C). Place the cabbage rolls in a baking dish, pour the sauce over them, and cover with aluminum foil. Bake for 25-30 minutes.

Remove from the oven, let cool slightly, and serve warm.