Preheat the oven to 375 degrees F. Line baking sheets with silpat mats or parchment paper.
In a large bowl, use an electric mixer to combine the peanut butter and margarine. Mix in the sugars, then mix in the eggs and vanilla. In a medium bowl, whisk together the flour, baking powder and baking soda. Mix in the dry ingredients, just until combined.
Roll tablespoonfuls of dough into balls and place them on the baking sheet (leave about 2 inches between each ball of dough). Use a fork to crisscross the ball of dough and gently press down.
Bake 9 to 10 minutes, just until the cookies are looking a little golden on the edges. Let them cool for about 10 minutes before removing them from the cookie sheets. Store in a covered container, or freeze for munching later.