In a mixing bowl, beat the eggs, sugar and vanilla until thick and lemon-colored (about 4 minutes). Combine the flour, baking powder and salt; add to egg mixture. Beat on low speed just until combined. Add the milk and butter; mix well. Pour into a greased 13x9x2-inch baking pan.
Bake at 350°F for 30 - 35 minutes or until a tooth pick inserted near the center comes out clean. Cool on a wire rack. Cut into squares. Cover and freeze overnight.
For frosting, in a mixing bowl, combine confectioner's sugar, milk, vanilla and salt; beat until smooth. Frost the top and sides of frozen cake squares; roll in peanuts. Place on wire racks to dry.