Clean the cauliflower and broccoli, cut into florets and wash. Blanch in bubbling salt water for about 5 minutes. Rinse in cold water and drain. Whisk cream cheese, milk and eggs well.
Season with salt, pepper and nutmeg. Grease an ovenproof dish with a little oil. Layer the broccoli and cauliflower florets and pour the egg milk over them. Coarsely grate the cheese and sprinkle over the gratin. Bake gratin in a preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: level 3) for approx. 30 minutes.