Preheat oven to 350 degrees.

In a medium skillet over medium heat, melt butter. When butter is melted, slowly swirl the pan and continue to cook the butter until it becomes a nice, brown-caramel color. The swirling helps it from burning. Remove from heat and allow to cool for 15 minutes.

When butter is cooled add to a large bowl and with the 1¾ cup light brown sugar and mix with electric mixer until no lumps remain, about 30 seconds.

Add egg, yolk and vanilla and mix for another 30 seconds until smooth.

Add in the flour, baking soda, baking powder and salt and mix on medium-low until incorporated.

Combine the ¼ cup brown sugar and ¼ cup granulated sugar coating together in a small bowl.

Roll cookie dough into balls and then roll in sugar mixture.

Place on lined baking sheet about 2 inches apart.

Bake at 350 degrees for 10-12 minutes or until edges begin to brown. Do not over-bake.

Transfer to wire rack to cool.

Once cooled make frosting. Combine brown sugar and butter in small saucepan over medium heat. Bring to a boil and continue cooking 1 minute. Remove from heat and cool for 10 minutes. Mixture will slightly thicken.

With hand mixer beat in milk until smooth. Slowly add in powdered sugar until spreadable consistency. You may need a little more or less than the 2 cups.

Spread about 1 tsp on each cookie. Makes 2 dozen.