On a cutting board, using a sharp knife, finely chop the onion, leek, garlic, and green pepper. Using the coarse side of a grater, grate the carrot and zucchini.
On the same cutting board, cut the chicken thigh fillets into very small pieces.
Place a deep non-stick pan over high heat and allow it to heat well. Add half of the olive oil.
Sauté the vegetables—the onion, carrot, leek, garlic, zucchini, and green pepper—for 3–4 minutes, seasoning with salt and freshly ground black pepper.
Remove the vegetables from the pan. Return the pan to high heat, add the remaining olive oil, and sauté the chicken thigh fillets, seasoning with salt and freshly ground black pepper.
Deglaze with the white wine, then add back the vegetables along with the chopped tomatoes, chicken stock, and parsley. Stir well and let the chicken simmer for 20–22 minutes, until the sauce thickens.
In a pot of salted water, boil the pasta until al dente. Drain, transfer to a bowl, add the olive oil and grated graviera cheese, and mix well.
For the béchamel sauce, place a saucepan over medium heat, add the butter, and once melted, add the flour. Stir until the two ingredients are well combined.
Gradually add the milk, stirring constantly with a whisk.
When the mixture starts to thicken, remove the saucepan from the heat and add the egg yolks, nutmeg, salt, and freshly ground black pepper, stirring quickly and vigorously.
Layer the pasta in a baking dish, spread the chicken and vegetable mixture evenly on top, and finish by spreading the béchamel sauce evenly over the surface.
Bake in a preheated oven at 190°C (fan) for 30–35 minutes.
