Place the carrots in the bottom of a medium-sized baking dish. Add the butter and a pinch of the garlic.
Sprinkle over some of the grated emmental.
Layer the swede over, and add a couple more knobs of butter, and a little more garlic. Repeat with the parsnips, and finally the potato.
Sprinkle over the remaining cheese.
Mix together the milk, cream and egg, and pour evenly over the vegetables.
Top with the breadcrumbs and bake the gratin in a preheated oven 190C/375F/Gas 5 for 45 minutes.
Serve.