Bring a pan of salted water to a boil. Remove the outer leaves and the stalk of the cabbage, rinse and simmer in the pan for 10 minutes.
Lift out cabbage, peel off the outer 4 leaves and continue to cook, possibly even 2-3 minutes. If too tight, lift out, rinse and drain leaves. Prepare 8 cabbage leaves. Cut the ribs flat and put each 2 leaves overlapping on a kitchen towel. Place steak tartare in a bowl. Clean mushrooms and finely chop. Peel shallots and very finely chop. Drain capers and chop coarsely. Knead mushrooms, shallots, capers and egg with tartare. Season with salt, pepper and thyme. From tartare mixture form 4 meatballs, put in the middle of the cabbage leaves and roll up into rolls. Wrap each roll with kitchen twine. Heat oil and butter in a large casserole.
Cook rolls over medium heat around 5 minutes. Add broth and tomatoes, cover and simmer for 30 minutes.
Remove rolls and set aside the pan with the sauce. Stir in cream without allowing to boil. Season with salt and pepper. Serve rolls with sauce and garnish with chives.