Preheat oven to 350°F (175°C). Line an 8x8 inch baking pan with parchment paper, leaving an overhang on the sides.
In a medium bowl, combine graham cracker crumbs and sugar. Pour in melted butter and stir until well combined. Press the mixture evenly into the bottom of the prepared baking pan.
Bake the crust for 10 minutes. Remove from oven and let cool slightly.
In a large bowl, beat cream cheese and sugar with an electric mixer until smooth. Beat in flour and vanilla extract.
Add eggs one at a time, beating well after each addition.
Pour the cheesecake filling over the cooled crust. Bake for 25-30 minutes, or until the edges are set and the center is still slightly jiggly.
Let the cheesecake bars cool completely in the pan on a wire rack. Then, chill in the refrigerator for at least 2 hours before cutting into bars.
Notes
Serve plain or with your favorite toppings like fruit or chocolate sauce.