Remove core from cabbage; place cabbage into large pot of boiling, salted water. cover and cook for 10 minutes, flipping cabbage halfway through cook time. Remove and set aside to cool.
Dice corned beef into bite sized pieces; sauté corned beef, onion, bell pepper, celery, and rice in olive oil.
In a large bowl, mix crushed tomatoes, sugar, and apple cider vinegar; spread 1 cup of the tomato sauce onto the bottom of a 9x13 baking dish.
Remove leaves from cabbage, fill each with 1/4 cup of corned beef mixture, and roll—starting from one end of the cabbage leaf and brining in the sides as you go. Placing each one in the baking pan as you go.
Pour remaining tomato sauce over top of cabbage rolls, cover pan with foil, and bake at 350 degrees for 1 hour. Remove foil and bake for an additional 15 minutes.