Preheat your oven to 350°F (175°C). Lightly grease an 8x8-inch baking pan or line it with parchment paper for easy removal.

In a medium bowl, mix together the graham cracker crumbs, 1/4 cup sugar, and melted butter until the mixture resembles wet sand. Press this mixture firmly into the bottom of the prepared pan to form an even crust.

Bake the crust for 10 minutes, then remove from the oven and let it cool slightly while you prepare the filling.

In a large mixing bowl, beat the softened cream cheese and 1/2 cup sugar together with an electric mixer until smooth and creamy, about 2-3 minutes.

Add the eggs one at a time, beating well after each addition. Mix in the lemon juice, lemon zest, and vanilla extract until the filling is smooth and well combined.

Pour the cheesecake filling over the baked crust, spreading it out evenly with a spatula.

Bake for 20-25 minutes, or until the center is just set and the edges are lightly golden.

Remove from the oven and let the bars cool completely at room temperature. Once cooled, refrigerate for at least 2 hours to allow the cheesecake to firm up.

Once chilled, use a sharp knife to cut the cheesecake into 12 bars.

For clean cuts, wipe the knife with a damp cloth between slices.