In a medium size mixing bowl sift together the flour, baking powder, salt and baking soda. Set aside.
Using an electric mixer cream together the softened butter, light brown sugar, granulated sugar, peanut butter and vanilla. Beat for 3 minutes until smooth, fluffy and light beige in color.
Add the eggs one at a time beating well after each addition. Stop to scrape the bowl periodically so all of the ingredients fully combine.
Add sifted dry ingredients gradually while beating on low speed, mixing well between each addition. Repeat until all of the dry ingredients have been added, stopping to scrape the sides of the bowl as needed. Beat just until the ingredients are fully combined
Use a large non-stick spatula to mix in the Reese's pieces and milk chocolate chips by hand. The batter will be stiff. Cover and chill for 30-60 minutes.
To bake: Preheat oven to 350°F. Line 2 baking sheets with parchment paper. Set aside.
Use a 2 or 4 oz ice cream scoop to separate the dough. Place the dough rounds at least 3-inches apart on the baking sheet. Press the centers to flatten slightly for even baking. Bake for 14-16 minutes or until lightly golden.
Cool on the cookie sheet for 5 minutes, then remove to a cooling rack to cool completely.