In a small sauce pan, melt the butter over medium heat. As soon as it melts and is simmering, begin stirring often. Watch the butter closely after its melted because the butter can go from browned to burnt, pretty quickly. You will notice a pleasant nutty smell, and see dark brown butter particles at the bottom of the sauce pan. The butter itself should be a nice light brown. Turn off the heat and keep stir a few times as its cooling. All the butter to cool completely in a seprate bowl in the refrigerator (about 25 minutes). It should solidify quite a bit. If it hasn't solidified much, allow a bit more time. (the freezer is okay too just don't actually FREEZE the butter).

Preheat your oven to 350 degrees F. Line your baking sheet with parchment paper.

In a large bowl, whisk the flour, baking powder and salt. Set aside.

In the bowl of an electric mixer, scrape the butter into the mixer bowl. Add the brown sugar and the granulated sugar and beat on high until fluffy, about 5 minutes. Scrape the sides, as needed.

Turn the mixer to low speed and add the eggs and vanilla. Once combined well, add the flour mixture and mix until everything looks smooth. Don't overmix.

Form the dough into equal 1" balls. Place on parchment paper covered baking sheet about 2" apart.

Use the bottom of a glass or flat object to press gently on top of the cookies, flattening them slightly.

Bake for approx. 8-10 minutes. The cookies will look a little under baked but the edges should look cooked. Do NOT over bake. You will wind up with a dry cookie at the end. Take out at the 8 minute mark if possible. Cookies will continue to cook as they cool. Allow to cool slightly before adding the frosting.

In a small sauce pan, repeat step 1 above with 1/3 cup butter. Melt the butter over medium heat. As soon as it melts and is simmering, begin stirring often. Remove from stove once butter is light brown. DO NOT allow to cool.

In the bowl of your stand mixer, beat the butter, powdered sugar, vanilla extract and 3 tablespoons of milk on low speed about 1 minute or until smooth.

Add a little more milk (the remaining tablespoon) and mix well until frosting is creamy and spreadable. Frost cookies while still warm, not hot.