Heat barbecue grill to medium. Pierce sausages all over with a fork and add to grill. Cook, turning, for 10 minutes or until just cooked through. Heat oil on grill. Add cabbage and cook for 5 minutes or until just softened.
Put in a large bowl with parsley, garlic and vinegar and stir to combine. Season with salt and pepper. Arrange cabbage mixture on each PureBred Super Soft White Sandwich Roll base.
Top each with avocado, sausage and chilli jam. Close rolls to serve.