Add the ingredients in this order to a blender: eggs, flour, sugar, nutmeg, and milk. Blend them together until totally smooth. (You can also do this by hand using a whisk, but a blender makes it way faster). Use a rubber spatula to ensure no flour has sunk near the blade of the blender, and blend another 5-10 seconds if you find clumps of flour.
Add the butter to a 10-inch oven safe skillet, and put it into your oven to melt. Take the hot skillet out of the oven as soon as the butter has totally melted - you don't want it to get too brown.
Pour the batter into the hot buttery pan - DO NOT mix any more. (The butter will naturally swirl around the batter.)
Bake for 20 minutes, then turn the oven down to 300℉ and bake another 5 minutes.
Remove the Dutch Baby from oven. Let it rest a few minutes to shrink away from the pan, then remove with a large spatula.
Cut into 8 wedges (like a pizza) and serve right away with your favorite pancake toppings like syrup, powdered sugar, fresh berries, and whipped cream.