Preheat the oven to 375°F (190°C). Bring a large pot of salted water to a boil.
Pound the chicken breasts to about ½ inch thick. Season both sides with salt and pepper.
Heat the avocado oil in a large skillet over medium heat. Cook the chicken for 5–6 minutes per side, until golden and the internal temperature reaches 165°F (74°C). Let rest for 5 minutes, then cut into bite-sized cubes.
Cook the ziti until al dente, about 1–2 minutes less than the package directions. Drain and set aside.
Melt the butter in a large pot over medium heat. Sauté the leek for 1 minute, then add the garlic and cook for another minute. Add the broccoli and sauté for 2–3 minutes, until tender.
Stir in the flour. Gradually add the milk, about 1 cup at a time, stirring well before each addition. Increase the heat to medium-high and cook until bubbling and slightly thickened.
Reduce the heat to medium and stir in the Parmesan, salt, black pepper, nutmeg, and cayenne.
Turn off the heat and stir in the cooked pasta and chicken. Transfer to a greased 9 × 13-inch baking dish or individual baking dishes. Top with mozzarella and Parmesan.
Bake uncovered for 20–25 minutes, until the cheese is melted and the top is golden brown in spots.
