Cook the cabbage in boiling salted water until just tender. remove from the heat and drain. When slightly cooled, chop fine.
Heat the oil in a large saucepan over medium heat. Add the onions, celery, and bell pepper. Cook, stirring often, until soft and golden, 5 to 6 minutes. Add the cabbage and cook, stirring often, until soft, about 10 minutes. Add the cream, butter, and the toasted bread crumbs and stir until the butter is completely melted. Season with salt and cayenne. Add the parsley and garlic. Mix well and pour the mixture into a large casserole.
Combine the cheese and fine dried bread crumbs and sprinkle evenly over the top. Bake at 350 degrees until heated through, about 30 minutes.