Cream butter and sugar until light and fluffy. Add vanilla and 1 egg at a time, beating well. In another bowl, whisk together flour, baking powder and salt; beat into creamed mixture alternately with milk. Transfer to prepared pan.
Bake until a toothpick inserted in center comes out clean, 40-45 minutes. Place on a wire rack; cool completely.
For frosting, beat butter until creamy; gradually beat in confectioners' sugar until smooth and light in color, about 3 minutes. Beat in vanilla and 3 tablespoons cream until light and fluffy, about 2 minutes; thin with additional cream if desired. Spread over cake.