Whisk the egg in a medium bowl. Add in the sugar, brown sugar, cinnamon, nutmeg, and salt. Whisk until smooth.
Gently whisk in the butter and vanilla.
Add the flour and whisk until fully incorporated.
Cover the bowl and set aside for 10 minutes.
Meanwhile, heat a pizzelle maker. Before adding the batter spray both sides with cooking spray.
Add one tablespoon of batter to the center of each pizzelle plate on the pizzelle maker. Close the maker and cook for 30 seconds. Check to see the doneness of the cookie. Close and cook for an additional 10 seconds if desired.
Using a long, flat icing spatula, pick up the pizzelle and place it gently on a wire rack to cool. Repeat with remaining batter.
Notes
Slightly adapted from Dorie's Cookies by Dorie Greenspan.