Peel the potatoes and cut into slices a few mm thick. Do the same with the carrots and courgette.
Press the garlic and mix with cream and milk. Season with cumin, salt, and pepper.
Grease an ovenproof dish with the remaining olive oil. Put in the slices of potato, courgette, and carrot, one after the other. Season each layer with salt and pepper. End with a layer of potatoes
Pour over the milk/cream mixture and sprinkle the cheese on top.
Cook in the oven for 45 to 60 minutes. The gratin is ready when you can easily insert a skewer.