Place the bread slices on a baking sheet lined with parchment paper. Drizzle with the white wine.
Carefully clean the leeks, cut away the roots and cut only the light green and white parts into fine rings. Remove the skin from the carrots. Cut off the stem of the zucchini. Grate both vegetables on the rösti grater.
Blanch leek, carrots and zucchini in a little boiling salted water for two minutes. Drain in a sieve, cool and drain well.
Grate the two cheeses on the grater. Chop the parsley. Mix these ingredients with the blanched vegetables and season with salt, pepper and nutmeg. Spread the mixture evenly on the bread slices.
Meanwhile, bake the cheese slices in the oven heated to 220 degrees on the second rack from the bottom for about twelve minutes. Bring to the table very hot.