Clean the fennel, putting the green aside for garnishing. Wash the fennel and cut small ones. Peel, wash and slice the carrots. Whisk egg and milk and season with salt and pepper.
Halve the salami slices. Put the vegetables and salami in a small casserole dish, add egg-milk. Sprinkle gratin with cheese and bake in a preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: level 2) for 30-35 minutes.
Garnish gratin with fennel green and serve immediately.