Preheat the to 350F degrees. Spray a pie dish or quiche with oil.
Evenly spread the broccoli in the dish and top it evenly with the ham.
Make the custard mixture by whisking together the milk, half and half, eggs, salt, black pepper, and the nutmeg.
Pour the custard into the dish and top with Swiss Cheese.
Bake 35 to 40 minutes, until the center is set.
Cut the quiche into 6 pieces and serve.
