Preheat the oven to 350°F (175°C) and line a 9x13-inch baking pan with parchment paper.
In a large bowl, whisk together flour, granulated sugar, baking powder, and salt. Cut in the cold butter until the mixture resembles coarse crumbs.
Add eggs and vanilla extract to the flour mixture, mixing until just combined. Press two-thirds of this mixture into the bottom of the prepared pan.
In a separate bowl, toss diced peaches with cornstarch and brown sugar until well coated.
Spread the peach mixture evenly over the crust layer. Crumble the remaining dough over the top.
Bake for about 35 minutes or until the top is golden brown. Allow to cool completely before cutting into squares.