Preheat oven to 350 F. Line a 9 x 13-inch baking pan with non-stick foil and lightly spray grease with butter or nonstick cooking spray.
In a small bowl, sift together flour, baking powder, and salt. In a medium bowl, cream together peanut butter, butter, brown sugar, and white sugar. Add eggs and vanilla, beating until combined. Add dry ingredients to peanut butter mixture and stir until combined. Add miniature chocolate chips and stir until incorporated. Pour into prepared pan and bake in preheated oven for 25 to 30 minutes. Remove from oven and immediately cover the top with the semi-sweet chocolate chips. Let chocolate stand until softened, then smooth evenly across the top. Let cool completely before cutting. Makes about 2 dozen bars, depending on size.