Cake: Preheat oven to 350 degrees. Cream butter and sugar until fluffy. Add eggs one at a time. Sift flour, baking soda, and salt together. Alternating, add flour and sour cream to butter mixture. Add vanilla. Pour into three 9-inch prepared pans. Bake for 25 to 35 minutes. Test with cake tester for doneness. Remove from oven and cool on racks for 10 minutes, then remove from pan for complete cooling.
Frosting: Melt butter; add brown sugar and milk. Cook 2 minutes over medium heat, stirring constantly. Remove from heat and add vanilla. Pour over confectioners' sugar and beat until smooth. Let cool slightly, then frost layers.