Place butter, sugar, salt, vanilla extract, ground cinnamon and nutmeg in the bowl of a stand mixer fitted with the paddle attachment. Cream until the mixture is smooth and creamy looking, about 2 minutes.
Stop the mixer and scrape down the bowl, thoroughly scraping the paddle attachment. Add all the flour at once. Turn the mixer to low speed and mix until just combined. The dough will come together into large ball after about 1 minute. Stir in carrots and nuts.
Turn dough onto a lightly floured surface. Use your hands to shape the dough into a rectangle and lightly flour the top of the dough. Do not use too much flour, just enough to keep the rolling pin from sticking.
Roll the dough ¼-inch thick. Use a 2-inch round cookie cutter to cut out the cookies. Place the cookies on a parchment-lined baking sheet. Prick each cookie in the center with a fork, to ensure steam is released as the cookies bake and keep a nice smooth top.
Reroll dough and continue to cut out cookies until all the dough has been used. You might have a small piece left over.
Chill unbaked cookies in the refrigerator for at least 30 minutes, up to 2 days. Chilling the dough will help the cookies hold their shape when baking. If chilling longer than 2 hours, cover tightly with plastic wrap to keep them from drying out.
Bake for 16-18 minutes. The bottom of the cookies will be lightly golden brown.
Shortbread cookies can be stored in an airtight container for 1 week.
Cream Cheese Glaze
Place cream cheese and powdered sugar in a small bowl. Mix with a wooden spoon or silicone spatula until smooth and creamy. Add 2 teaspoons each milk and orange juice. If the glaze is too thick to drizzle, add either milk or orange juice 1 teaspoon at a time until the desired consistency is reached.
Drizzle over the cookies.
Once the glaze is added to the cookies, the cookies will need to be stored in the refrigerator in an airtight container.
