Wash cabbage leaves and remove tough stems from the bottom. Bring water to a boil and cook leaves for 3 to 4 minutes until softened. Drain well and set aside.
Cut mushrooms in slices.
Heat oil in a skillet and fry onions for about 2 minutes, then add the garlic for about 2 minutes and add minced meat, steer until the meat is cooked.
Add soy sauce and honey and mix all together.
Mix well and divide into 10 portions. Place a portion of the mixture onto the center of each cabbage leaf.
Roll the leaf around the filling. Fasten the rolls with toothpicks. Place in a baking sheet.
For the sauce, combine the tomato sauce, tomatoes, sugar, vinegar, and 1/2 cup of water; heat for 10 minutes and cover the rolls with the sauce. Bake in the preheated oven for about 20 minutes (180 degrees).