Preheat the oven to 350 degrees Fahrenheit and prepare a baking sheet with parchment paper or non-stick cooking spray.
In a large bowl, mix together the flour, salt, brown sugar, baking powder, and nutmeg until everything is evenly combined.
In another bowl, whisk together the egg and vanilla extract until they are well incorporated.
Add the milk to the egg mixture, stirring continuously until it forms a homogeneous liquid.
Pour the wet ingredients into the dry mixture and stir with a spoon until everything is evenly combined.
Cut the butter into small cubes and add them to the mixture, stirring until the butter has melted and been incorporated into the batter.
Grease your baking sheet with butter or non-stick cooking spray.
Using a spoon, scoop out portions of the batter onto the baking sheet and bake for 25 minutes or until golden brown.
Allow the buns to cool before serving.