Begin by beating the sugar and butter together in a large bowl with an electric mixer until the mixture is light and fluffy. Gradually add the eggs, one at a time, ensuring that each is thoroughly incorporated before adding the next. Once the eggs are well combined, stir in the vanilla extract.
In a separate bowl, mix the flour, baking soda, salt, and nutmeg. Gradually add this dry mixture to the creamed butter and sugar, stirring until fully combined.
Turn the dough out onto a lightly floured surface and knead it for a few turns until it becomes smooth and uniform in texture.
Cover the dough and refrigerate it for approximately 30 minutes to allow it to firm up.
Preheat the oven to 325°F (165°C).
Roll the dough out to a thickness of about ¼ inch on a floured surface. Use cookie cutters to shape the dough, and place the cut cookies about 1 ½ inches apart on baking sheets.
Bake the cookies in the preheated oven for 8 to 10 minutes, or until the edges turn a light golden brown.
Once baked, allow the cookies to cool slightly on the baking sheets before transferring them to a wire rack to cool completely.
