Add walnuts to a dry skillet over medium heat. Toast for 5 to 10 minutes, and remove from heat to cool. Set aside. 

Drain the maraschino cherries and dry on a paper towel, cut into quarters and pat dry. Set aside. 

To brown butter, add butter to a medium saucepan. Melt over medium heat stirring until the butter begins to froth and foam. Brown flecks will form on the bottom on the pan and the butter will smell toasted. Be careful to not walk away, as this burns quickly. 

Reserve 1/4 cup of the butter for the frosting and pour the remaining butter into the bowl on an electric mixer.

Add the sugars to the butter and mix until smooth and combined, about 2 minutes. Add eggs and vanilla and continue to mix until smooth. Add flour, baking powder, and salt. Mix until you can no longer see the flour. Fold in cherries, chocolate chips, and walnuts. 

Chill the dough for one hour or overnight. 

When ready to bake, preheat the oven to 350°. Scoop the dough onto baking sheets lined with parchment. Bake for 8 to 10 minutes, Let cool on the sheets for 5 minutes, then transfer to a wire rack to cool completely.

To make the frosting, add powdered sugar to the reserved brown butter that is at room temperature. Mix and add vanilla and milk. Mix until the frosting is smooth and spreadable. Add more milk or powdered sugar to get the desired consistency as needed.