Preheat the oven to 425°F. Place an oven-safe skillet, such as cast iron, into the oven and let it preheat for at least 8 minutes.
Meanwhile, in the jar of a blender, combine eggs, flour, milk, sugar, salt, nutmeg, and vanilla, and blend for 30 seconds on high speed until smooth, scraping down the sides of the blender halfway through to ensure all the flour is incorporated.
Carefully remove the pan from the oven using hot mitts. Add 3 Tbsp of butter to the hot pan and swirl it to coat the bottom and sides of the pan. The butter should sizzle.
Add the batter to the buttered pan, then bake for 16-18 minutes or until the pancake is puffed and golden brown at the edges.
Carefully remove the pan from the oven with hot mitts and serve the pancake right away.
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