Preheat oven to 400ºF (200ºC).
Shred the cabbage by cutting the cabbage head in half and slicing it with a sharp knife into thin cabbage noodles.
Heat a large frying pan or ovenproof skillet on medium-high heat. Add the cabbage and a splash of water. Toss it around with a tong and cook until the cabbage is soft. Remove from the pan and drain.
Return the same pan to the stove and add the olive oil. When hot, add garlic and onion. Fry until it starts to get soft and translucent.
Add the ground meat to the pan. Fry while breaking the meat up using a spatula. Season with salt, ground black pepper, basil, and oregano. Add the crushed tomatoes and the cooked cabbage when the meat starts to get brown. Give it a good mix and let it simmer for a couple of minutes while you prepare the cheese sauce.
Mix the heavy whipping cream, cream cheese, garlic, salt, and pepper in a bowl until smooth.
Pour it on top of the meat and cabbage mixture. Sprinkle the cheese on top. Bake in the oven for 20 minutes or until the cheese has a golden color.
Let it cool a bit before serving. Garnish with fresh basil.