Preheat oven to 350˚F. Grease a 10-inch pie dish with butter and set aside.

Bring a large pot of generously salted water to a boil. Add the broccoli and cook just 1-2 minutes, until crisp-tender. Drain and rinse in cold water to stop the cooking. Pat dry, and arrange in an even layer in the pie dish. Top with the grated cheese.

Whisk together the milk, cream, eggs, and nutmeg until smooth. Sprinkle with salt and pepper to taste, and whisk to incorporate. Gently pour the egg mixture over the broccoli. Bake for 35-40 minutes, until the center has set. It's fine if it's still a bit wobbly, as it will continue to cook when you remove it from the oven. Set aside to cool for 10 minutes before serving.