Optionally, let eggs, milk, and butter come to room temperature.
Preheat oven to 425F / 220C. Put a heavy 9-inch / 23-centimeter diameter, pan on the middle rack of the oven to heat. Let the pan heat in the oven for at least 15 minutes so it is very hot.
Put eggs, flour, half and half or milk, flour, sugar, salt, nutmeg, and vanilla in a blender and mix for 30 seconds. Alternatively, put the ingredients in a bowl and mix until smooth. The batter should be very thin.
Remove the pan from the oven and add the butter to the pan. The heat from the pan should be enough to completely melt the butter. If not, return the pan to the oven or heat over the stovetop until the butter is melted.
Add the batter to the heated pan with butter, and cook for 25 minutes.