Mix the flour, ground nuts, salt and nutmeg in a medium bowl and set aside.
Beat the butter and sugar until light and fluffy, about 1-2 minutes if using a hand mixer, or 3-4 minutes if using a stand mixer. Scrape the bottom and sized of the bowl as you go.
Add the egg and vanilla extract and mix to combine.
Mix in the flour mixture with the mixer on low speed. Mix until the flour has been incorporated and you have a smooth dough.
Divide the dough into two, wrap part with plastic wrap and refrigerate for minimum 1 hour.
Roll the dough between two pieces of parchment paper into 1/8-inch thick. Refrigerate or freeze for 10 minutes to allow the butter to set again.
Use a round cookie cutter (2-inches) with rides to cut the dough.
Transfer the cut cookies to the prepared pan, and use a smaller cookie cutter (you can also use a piping tip) to cut half the cookies in the center.
Place the pans back in the refrigerator while the oven warms to 350F (180C).
bake for 15-17 minutes, until the cookies are light golden brown.
Remove from the oven and allow to cool completely before assembling.