In a large mixing bowl, BEAT butter and peanut butter with an electric mixer on medium-high speed for 30 seconds.
ADD granulated sugar, brown sugar, baking soda and baking powder; BEAT until combined, scraping sides of bowl occasionally.
ADD egg and vanilla; BEAT until combined; continue to BEAT with mixer while adding flour; when mixture becomes too stiff for mixer, STIR in remaining flour by hand.
COVER dough; CHILL until easy to handle, about 1 hour.
PREHEAT oven to 375°.
SHAPE dough into 1" balls; ROLL balls in granulated sugar to coat.
PLACE dough balls about 2" apart on an ungreased cookie sheet; using a fork, flatten balls by making criss-cross marks on top.
BAKE until cookie bottoms are light brown, about 7 to 9 minutes; TRANSFER cookies to a wire rack to cool.
Per Serving (excluding unknown items): 2888 Calories; 164g Fat (49.8% calories from fat); 56g Protein; 316g Carbohydrate; 12g Dietary Fiber; 460mg Cholesterol; 2515mg Sodium. Exchanges: 9 1/2 Grain(Starch); 4 1/2 Lean Meat; 29 1/2 Fat; 11 1/2 Other Carbohydrates.