Preheat the oven to 375 degrees.
Cream the butter and brown sugar together in a large bowl until smooth.
Add in the egg and mix well.
Stir in the sour cream and mix until combined.
In a medium bowl combine the flour, baking soda, and salt. Mix well.
Add the flour mixture to the brown sugar mixture and mix until a dough forms.
Drop by tablespoon onto a cookie sheet 2 inches apart.
Bake for 9-11 minutes or until the edges begins to brown.
Remove from the oven and allow to cool for 2 minutes. Remove to a wire rack to cool completely.
Meanwhile, heat the butter and brown sugar in a small saucepan over medium heat. Mix until the butter is melted and the brown sugar is melting.
Slowly stir in the milk. It may look like it is starting to curdle but keep on stirring. Bring this mixture to a boil, stirring constantly, and then remove from heat.
Whisk in the powdered sugar until combined.
Allow the frosting to cool for 10 minutes or so. The original recipe says to allow it to cool for 20-30 minutes but I found it was too hard to spread after that amount of time.
Spread the frosting on the cookies and enjoy!