Beat butter or margarine, peanut butter, 1/2 cup granulated sugar and brown sugar together until fluffy. Beat in egg. Sift flour and baking powder together; stir into butter mixture. Chill dough thoroughly, 2 to 3 hours.
Preheat oven to 375 degrees F (190 degrees C).
Roll dough into 1-inch balls. Press a chocolate-covered caramel into the middle of each ball. Roll dough around it. Roll each ball in granulated sugar. Place 2 inches apart on ungreased cookie sheets. Bake for 10 minutes or until golden brown. Let cool 2-3 minutes, then remove from cookie sheets.
