Preheat the oven to 350 degrees F. Line two baking sheets with non stick baking mats or parchment paper.
Place the butter, granulated sugar and brown sugar in the bowl of a mixer. Beat for 2-3 minutes or until light and fluffy.
Add the Eggland's Best eggs, eggnog and vanilla extract to the bowl. Beat for 1-2 minutes or until well combined.
Add the salt, baking soda, nutmeg and flour to the bowl. Mix on low speed until just blended.
Spoon tablespoon sized dollops of the dough 2 inches apart on the prepared pans. You may need to repeat this process if you have more dough left over.
Bake the cookies, one pan at a time, for 10-13 minutes or until golden brown around the edges. Repeat with remaining pan of cookies.
Let the cookies cool on the pan for 5 minutes, then transfer to a rack until completely cool.
For the frosting, place the butter in the bowl of a mixer and beat until light and fluffy. Add the eggnog and beat until smooth.
Add the powdered sugar and salt, then beat on low speed until frosting is smooth and fluffy. You can add more eggnog, one teaspoon at a time, to reach your desired consistency if needed.
Spread a layer of frosting onto each cookie, then top with sprinkles and serve.