Peel parsnips and carrots and quarter or halve lengthwise depending on size. Cut leek into small slices. Slice onion. Melt butter in frying pan. Add vegetables, and season to taste with salt and pepper. Add about 50 ml water. Simmer covered on medium heat 10-15 minutes.
Whisk eggs, then mix in milk and sour cream. Stir in horseradish, lemon zest, thyme and Gruyère AOP. Season to taste with salt and pepper.
Place vegetables in gratin dish. Pour liquid mixture on top. Bake on middle rack in oven preheated to 180° C. for around 35 minutes.