Preheat oven to 350F, Combine flour, baking powder and salt in small bowl. Beat butter in large bowl with electric mixer at medium speed until smooth. Gradually beat in brown sugar; increase speed to medium high until light and fluffy.
Beat in eggs, 1 at a time, until fluffy. Beat in vanilla. Gradually stir in flour mixture until blended. Stir in the peanuts until blended.
Drop 1 tbsp. of dough about 1 inch apart onto parchment lined baking sheets; flatten slightly with hands. Bake 12 minutes or until set. Let cookies stand on sheets 5 minutes; transfer to wire racks to cool completely. Dust cookies with powdered sugar. Store in airtight container. Makes 30 cookies