Preheat oven to 350º. Beat butter and peanut butter at medium speed with an electric mixer until creamy; gradually add sugars; beating well. Add egg and vanilla; beat well.
Stir together flour, baking powder, and salt. Add to butter mixture; beat at low speed until well blended. Stir in chocolate chunks. (If desired, store dough in an airtight container in refrigerator up to 1 week.)
Drop cookie dough by heaping tablespoonfuls 2 inches apart onto parchment paper-lined or lightly greased baking sheets.
Bake at 350º for 11 to 12 minutes or until edges of cookies are brown. Bake chilled dough 13 to 14 minutes.) Cool on baking sheets on a wire rack 3 minutes; transfer to wire racks, and cool completely (about 30 minutes).