Beat butter at medium speed with an electric mixer until creamy; gradually add sugars, beating well. Add egg and vanilla, beating until combined.
Combine flour, baking powder, and salt; gradually add to butter mixture, beating until blended. Stir in oats and remaining ingredients. Drop by rounded tablespoonfuls onto ungreased baking sheets.
Bake at 375° for 10 minutes or until lightly browned. Cool cookies on baking sheets 1 minute; remove to wire racks to cool completely.