Prepare the cabbage: Carefully remove 10-12 large outer leaves from the Napa cabbage. Bring a large pot of water to a gentle boil and blanch the leaves for 1-2 minutes until just pliable. Immediately transfer to an ice bath, drain, and pat dry.
Make the filling: In a large bowl, combine the ground meat, cooked rice, diced onion, grated carrots, minced garlic, grated ginger, soy sauce, sesame oil, beaten egg, scallions, and cilantro if using. Season with salt and pepper and mix thoroughly but gently.
Roll the cabbage: Place about 3-4 tablespoons of filling near the stem end of each cabbage leaf. Fold the stem end over the filling, fold in the sides, and continue rolling to form a neat package. Place seam-side down in your baking dish.
Prepare the sauce: Whisk together the broth, soy sauce, rice vinegar, honey or brown sugar, and sesame oil in a bowl. Pour over the cabbage rolls, covering them about halfway.
Bake the rolls: Cover the baking dish with foil and bake at 375°F (190°C) for 35-40 minutes. Remove the foil and bake for an additional 10 minutes until the tops are slightly golden.
Thicken the sauce (optional): If you prefer a thicker sauce, carefully pour the cooking liquid into a small saucepan. Add the cornstarch slurry, bring to a simmer, and cook until thickened, about 2 minutes. Pour back over the rolls.
Serve warm: Garnish with additional chopped scallions and serve immediately, spooning some of the sauce over each serving.