Peel garlic and chop finely. Wash the rosemary, dab dry, remove the needles and chop finely. Heat milk and sour cream with garlic and rosemary in a saucepan, stirring occasionally. Season vigorously with salt and pepper.
Preheat oven (electric cooker: 175 °C/circulating air: 150 °C/gas: see manufacturer). Grease an ovenproof dish. Grate the cheese. Peel and wash parsnips and slice or cut them into thin slices. Peel and wash potatoes and slice or cut them into thin slices.
Layer potato and parsnip slices in the casserole dish. Finish with a layer of potatoes. Pour hot sour milk over it and sprinkle with breadcrumbs and cheese. Bake in a hot oven for 1-1 1⁄4 for hours, covering after 1 hour if necessary.