Preheat the oven to 170 °C. Grease a medium sized oven dish with butter.
Peel the parsnips. Cut into slices of approx. 3 mm thick. Beat the cream with the eggs. Press the garlic. Add to the egg mixture with the Herbes de Provence.
Arrange the parsnip slices in overlapping layers in the oven dish. Season with salt and pepper. Pour over the gg mixture. Bake the gratin in the middle of the oven for approx. 35 minutes until golden brown and cooked.