In a large bowl beat butter and sugar using an electric mixer until creamy. Add eggs, 1 teaspoon vanilla extract, and sour cream. Beat until smooth. Add baking soda, baking powder, and flour and beat on low until combined. The dough will be soft.
Preheat the oven to 350 degrees F. Line baking sheets with parchment paper. Drop heaping tablespoonful of the dough onto the baking sheets, 2-3 inches apart. Place into the oven and bake for 10-12 minutes, until the edges are golden brown and the center is set.
To prepare the frosting- Beat butter using an electic mixture until smooth. Add powdered sugar, 1 teaspoon vanilla extract, and milk. Beat until smooth. If the batter is too thick you can add a little milk as needed to thin it out. If it is too thin you can add more powder sugar until the desired consistency is reached.
Allow the cookies to cool and then top with frosting.