Place the butter in a medium saucepan. Cook over medium heat until the butter melts and begins to foam.

Continue cooking, stirring occasionally, until brown specks begin to form at the bottom of the pan and the butter has a nutty aroma. Remove the pan from the heat and allow to cool. If desired, strain the butter to remove the browned bits.*

Combine the flour, sugar, brown sugar, salt, baking powder, and baking soda in a large bowl. Add the cooled brown butter, water, buttermilk, vanilla, and eggs. Stir until smooth.

Spread the batter evenly in the prepared pan.

Bake 15 to 18 minutes, or until a pick inserted into the center comes out clean. Cool completely in the pan on a wire rack.

Using an electric mixer on medium speed, beat the butter until creamy. Gradually add the confectioners' sugar and 6 tablespoons of the sour cream. Beat until smooth. Add the remaining sour cream, a tablespoon at a time, if necessary to achieve a spreadable consistency.

Spread the frosting evenly over the cake. If using, sprinkle the nuts over the frosting.