Melt the butter in the microwave or in a saucepan and let it cool down a bit.
Mix together the flour, baking powder, baking soda and salt and set aside.
Combine the melted butter, and both sugars in a large mixing bowl. Stir well, then stir in the peanut butter, egg and vanilla. Add the flour mixture and stir until blended, then stir in the peanut butter chips. At this point, dough should be stiff enough to mold, but if it's not, chill it for about 10 minutes.
Scoop up large balls of dough (a little less than 1/4 cup each) and put on two plates or a large cookie sheet. Shape into neat balls, then use a fork to make a criss-cross pattern so that you have thick discs with criss-crosses. Chill for an hour or until cold and stiff.
Preheat oven to 375 degrees F. and line two baking sheets foil.
Arrange six criss-cross discs on each baking sheet and bake one sheet at a time on center rack for about 14 minutes or just until edges start to brown. Let cool on baking sheets for about 5 minutes, then transfer to a rack to cool completely. In my opinion, these are best when they are completely cool and crisp.