Add 2 cups of unsalted butter to a medium-sized saucepan and turn the heat on high. Allow the butter to boil, and then listen closely. Once the butter stops making popping noises, it should be done. When you stir, you will see brown flecks and smell a nutty aroma. Immediately remove from heat so that you do not burn the butter.
In a standing mixer with the paddle attachment, add 1 cup of browned butter and reserve 1 cup of browned butter, placing it in the freezer to chill.
Add 1 ½ cups brown sugar to the standing mixer. Mix until combined.
Add in 2 eggs and 1 tsp of vanilla. Mix until combined.
In a large bowl add 2 ½ cup all-purpose flour, 1 tsp baking soda, ½ tsp baking powder and ½ tsp fine sea salt.
Turn the mixer on low and slowly pour in the dry ingredients. Once a dough forms, stop the mixer.
Scoop the cookie dough using a standard-size cookie scoop onto light-metal-colored cookie sheets lined with parchment paper.
Bake the cookies for 8-9 minutes. Remove and allow the cookies to rest on the pan for 5-10 minutes before removing to a wire rack to finish cooling.
Frosting
Remove the reserved 1 cup of browned butter from the freezer and scoop it into the bowl of a standing mixer with the paddle attachment.
Beat until softened.
Add 3 cups powdered sugar, 1 tsp vanilla extract, and 1 tbsp heavy cream. Beat until combined. Turn the mixer on high and beat for 2 minutes until light and fluffy.
Spread the frosting on the backside of 1 cookie and place another cookie on top to create a cookie sandwich. Repeat until all 10 sandwiches are assembled.