In a large bowl, whisk together the eggs, milk, vanilla and granulated sugar until smooth and well combined. Add the flour, baking powder, baking soda, salt, nutmeg, cinnamon and unsalted butter. Stir until well combined. The dough will be soft and very stick. That's okay.
Turn out the dough onto a well floured work surface. It might be easier if you cut it in half. Roll out with a floured rolling pin or pat it out with your hands to about 1/2 an inch thick. Cut into 3-inch rounds with a small hole in the center. Transfer to a baking sheet lined with parchment paper.
Preheat your waffle iron on it's highest setting. Once hot, lightly grease with cooking spray and then place one to two doughnuts on, close and cook until golden brown and crispy. Transfer to a wire rack set over a baking sheet while you continue to cook the rest.
In a shallow dish, combine the sugar, vanilla bean seeds, pod and cinnamon until well incorporated. Use the back of your spoon to really work in the seeds into the sugar.
Dip each doughnut into the melted butter, and then into the sugar, turning over to coat both sides. Eat right away or store in an airtight container at room temperature for 2 days. These doughnuts are a bit firmer and dryer than normal, but it makes them great for dipping into coffee, hot chocolate or melted chocolate like you would churros!