Preheat the oven to 375 degrees F.
Finely shred the cabbage. Cut the bacon into 1/2-inch chunks. Place a small skillet over medium-low heat and fry the bacon, until crisp. Remove from pan with a slotted spoon and drain on paper towels. Set aside.
Add 1 tablespoon butter to bacon fat in frying pan. When it has melted add 1/2 the garlic and give it a quick stir with a wooden spoon to soften. Add the cabbage and coat it with the butter. Slowly let it wilt. Add the bacon. Season with salt and freshly ground black pepper. Remove from heat and add most of the chives, reserving a little for the garnish.
Generously butter the bottom and sides of a 9 by 13-inch ovenproof casserole dish. In a large bowl, combine the potatoes, 1 1/2 cups of cream, 1 cup of Parmesan, and the remaining garlic. Season with salt and freshly ground black pepper. Using your hands, place a layer of potatoes in the casserole dish. Sprinkle with Parmesan and repeat with 2 more layers. Spoon the cabbage mixture on top and spread it out evenly over the potatoes. Top it off with 2 more layers of potato and Parmesan. Pour the remaining 1 cup cream over the dish. Sprinkle with the remaining Parmesan.
Cover dish with aluminum foil. Bake for 1 hour. Remove foil and bake for 30 minutes until golden brown. Leave for 10 minutes before serving. Garnish with fresh chives.
*Cook's Note: Slice the potatoes immediately before using so they don't turn brown.