1. Peel the leeks, remove the base, and finely slice them. Heat 20g of butter in a saucepan and cook over low heat until they are tender (15-20 min). Season with salt and pepper.
2. Melt the remaining butter in a saucepan. Add the flour, mix, and cook for 2 min. Gradually pour in the cold milk while whisking with a hand whisk. Season with salt, pepper, add nutmeg, and continue cooking while stirring until the béchamel sauce is thick. Add the leek whites and mix.
3. Cut the chicken into small pieces. Heat olive oil in a frying pan and sauté the chicken until golden, then add it to the leek and chicken béchamel sauce.
4. Preheat the oven to 200 °C (392 °F).
5. Place a layer of lasagna sheets in the bottom of a buttered gratin dish. Pour a layer of leek and chicken béchamel sauce over it. Follow with a layer of grated gruyère cheese. Repeat the process 3 or 4 times, ending with the gruyère cheese.
6. Bake for approximately 30 min.