To a large skillet, add the 3/4 cups of butter (1 1/2 sticks). Cook over medium-low heat, stirring often, until the butter begins to brown and brown bits form on the bottom of the pan. Remove from heat immediately and transfer to a container. Let cool for about 30 minutes and then cover and refrigerate until it is still soft, but solid.
Preheat your oven to 350 degrees F and line to large cookie sheets with parchment paper or silicone baking mats. Set aside.
In the bowl of your stand mixer, with paddle attachment fixed, add the brown butter, brown sugar and granulated sugar. Mix until smooth and creamy. Add the egg yolks and mix again until fully combined. Add the vanilla extract and eggnog and mix again until incorporated.
In a medium bowl, whisk together the flour, baking powder, salt, cinnamon, nutmeg, and ground cloves. With the mixer speed set on low, gradually add the dry ingredients. Continue mixing until just incorporated.
Using a tablespoon-sized scoop, dollop the cookies on the prepared cookie sheets. Place in the oven and bake for 12-15 minutes or until just set around the edges. Remove from heat and let the cookies cool on the pan for 2 minutes before transferring to wire racks to cool the rest of the way.
While the cookies are cooling, prepare your frosting. In the stand mixer, with paddle attachment fixed, add the 1/2 cup unsalted butter, eggnog, vanilla extract, nutmeg, salt and confectioner's sugar. With the mixer speed set on low, mix the ingredients until fluffy.
Spread the frosting on the cookies and store in an airtight container for about a week. Enjoy!