Bring a large pot of water to boil.
Preheat oven to 350°F.
Core the cabbage carefully.
Place cabbage in boiling water.
Remove softened leaves gently.
Trim thick stems if needed.
Mix beef, rice, onion, and garlic.
Add egg, parsley, salt, and pepper.
Stir mixture until just combined.
Place filling on each cabbage leaf.
Roll tightly and tuck edges in.
Arrange rolls in baking dish.
Combine all sauce ingredients in saucepan.
Simmer sauce for 10 minutes.
Pour sauce evenly over rolls.
Cover dish with foil.
Bake for 1 hour 15 minutes.
Let rest before serving.