Begin by combining the all-purpose flour, salt, baking soda, and ground nutmeg in a medium-sized mixing bowl. Ensure the dry ingredients are well-integrated.

In a separate, larger bowl, cream the unsalted butter and granulated sugar together. Use an electric mixer set to high speed, and mix until the combination achieves a smooth and consistent texture, approximately 4-5 minutes.

Reduce the mixer's speed to a lower setting. Proceed to incorporate the egg and vanilla extract into the butter and sugar mixture.

Gradually introduce the previously combined dry ingredients to the wet mixture, ensuring they blend seamlessly.

Transfer the resulting dough to a refrigerated environment and allow it to set for 30 minutes.

Preheat the oven to a temperature of 325˚F (163˚C). Concurrently, portion the dough into 12 equal sections. Utilize your hands to shape each section into a spherical form.

Arrange the dough spheres on a baking sheet, ensuring they are spaced approximately 1 1/2 inches apart. Gently depress the top of each sphere using the base of a clean cup or similar flat implement.

Bake the formed cookies in the preheated oven for a duration of 10 minutes. The baking process is complete once the peripheries of the cookies attain a light golden hue.