Preheat oven to 350 degrees F (175 degrees C). Line 2 large baking sheets with parchment paper.
Mix flour, baking powder and salt in a medium bowl.
In a large bowl, beat butter, peanut butter, and vanilla with an electric mixer until well blended. Beat in both sugars. Scrape down the sides of the bowl. Stir in half of the dry ingredients into the mixture. Add eggs one at a time, blending well after each addition. Mix in remaining ingredients. Stir in peanut butter chips.
For each cookie, roll 1 heaping tablespoon full of dough into 1 3/4 inch diameter ball. Arrange balls 2 1/2 inches apart on prepared baking sheets. Using the back of fork, flatten dough balls and form a crosshatch on tops.
Bake cookies until dry on top, about 15 minutes.
Cool cookies on baking sheets for 5 minutes. Using a spatula, transfer cookies to cooling racks to cool completely.