Preheat oven to 350°F (180°C). Whisk together all-purpose flour, whole-wheat flour, baking powder, baking soda and salt. In another bowl, with hand mixer, beat butter with both sugars until light and fluffy. Beat in peanut butter, eggs and vanilla. Stir in flour mixture until combined. Stir in peanuts.
Roll dough into 1-in. (2.5-cm) balls. Place on parchment lined baking sheets about 2 in. (5 cm) apart. Dip a fork in flour and press a criss-cross pattern on top of each ball, flattening dough slightly. Bake for 14 to 15 min., or until tops are set and bottoms are golden brown, rotating half-way through baking for even cooking.
Cool cookies on baking sheets 2 min. Transfer to wire racks to cool completely. Store in airtight container up 2 days or freeze up to 2 weeks.
Substitute smooth peanut butter and/or add chocolate chips to dough.