Combine the graham cracker crumbs, flour, and brown sugar in a bowl. Scatter the butter over the top and cut in with a fork or pastry blender until the mixture resembles fine meal. Add the egg and stir just until the mixture comes together.
Transfer the mixture to the prepared pan and press into the bottom to form a crust. (This is a sticky endeavor. I've found using a rubber spatula helps spread the mixture more evenly.)
Bake until the top of the crust is just firm to the touch, 17-20 minutes. Let cool completely in the pan on a wire rack.