Grease and lightly flour a 13x9x2-inch baking pan; set aside.
In a bowl, stir together flour, baking powder and salt. In a saucepan, heat milk and butter together till butter is melted. Let cool slightly.
In a medium mixing bowl, beat sugar and egg with electric mixer till combined. Beat in milk mixture. Beat in flour mixture till just combined. Spread evenly in prepared pan.
Bake in a 325 degree F oven 20 to 22 minutes or till browned and firm when touched. Cool in pan on a wire rack.
Prepare frosting. Cut cake into 24 bars, making 7 cups crosswise and 2 cuts lengthwise. For each bar, frost top and sides; roll in peanuts. Frost bottoms; roll in peanuts.
Beat together butter, milk, vanilla, salt and 1 cup of the confectioner's sugar in medium-size bowl until smooth and creamy. Gradually beat in the remaining 3 cups sugar, or until good spreading consistency is reached.