Place first 4 ingredients in a large bowl; beat with a mixer at medium speed until well blended (about 2 minutes). Add peanut butter, beating well. Beat in egg and egg white.
Weigh or lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, baking powder, and salt, stirring with a whisk. Gradually add flour mixture to peanut butter mixture, beating until blended (batter will be thick). Spread batter evenly in a 13 x 9-inch metal baking pan coated with cooking spray.
Bake at 350° for 26 to 28 minutes or until a wooden pick inserted in center comes out clean.
Place chocolate in the top of a double boiler set over slightly simmering water; melt chocolate chips, stirring until smooth. Spread chocolate evenly over top. Cool completely on a wire rack. Cut into bars.