In a large mixing bowl with an electric mixer on low speed, combine the flour, brown sugar, peanut butter, and butter. Beat just until crumbly. Reserve one cup; set aside.
To crumb mixture in the mixing bowl, add the baking powder, baking soda, milk, vanilla, and eggs. Beat on low speed until moistened, then beat at medium speed for 3 minutes, scraping sides and bottom of bowl several times.
Pour the batter into the prepared baking pan.
Sprinkle the reserved crumbs evenly over the top of the batter and then sprinkle the chocolate chips evenly over crumbs.
Bake the cake for 35 to 40 minutes, or until a toothpick inserted in center comes out clean.