Peel, wash and slice the potatoes. Peel and roughly chop the onion. Cut ham into cubes. Grease a small gratin dish (18 cm Ø). Layer potatoes and ham.
Season with salt and pepper. Sprinkle onions over it. Peel the garlic and press it through a garlic press. Mix cream and garlic and season with salt and pepper. Pour over the potatoes.
Cook in the preheated oven (electric cooker: 200 °C/ gas: level 3) for 35-40 minutes. In the meantime, grate the cheese finely and sprinkle it over the potatoes about 20 minutes before the end of the cooking time. For the raw vegetables, peel and coarsely grate the carrots.
Mix lemon juice and honey. Coarsely chop the walnuts. Mix the raw vegetable ingredients. Serve gratin to taste, garnished with parsley. Add raw vegetables.