Preheat oven to 350. Mix flour, baking powder and salt in medium bowl; set aside. Using electric mixer, beat butter, margarine, peanut butter and vanilla in large bowl until well blended. Beat in both sugars. Scrape down sides of bowl. Beat in eggs one at a time. Gradually add flour mixture; mix until combined.
For each cookie, roll 1 tablespoonful of dough into a ball (smallest cookie scoop works well). Arrange dough balls on prepared baking sheets. Using back of fork, flatten dough balls and form crosshatch design on tops. Bake cookies until dry on top and golden brown on bottom, about 10 minutes. Cool cookies on baking sheets 5 minutes. Using metal spatula, transfer cookies to racks and cool completely. (Can be prepared up to 3 days ahead. Store in airtight container at room temperature.)