Steam the broccoli until tender. Mix the cooked chicken and broccoli in a large bowl and set aside.
Melt the butter in a saucepan over medium heat. Mix in the flour to form a roux. Cook, stirring constantly for 3 minutes. Add the half and half and heat, stirring constantly, until the sauce just begins to thicken.
Add the Maasdammer a little at a time, letting it melt between additions. Add the nutmeg and salt and pepper to taste.
Spread the chicken mixture into an oven proof casserole dish. Spread Parmesan evenly over the top.
Bake for 25 to 30 minutes or until golden brown and bubbly.