Preheat your oven to 350°F (175°C). Line the bottom of a 9x9-inch baking pan with parchment paper, leaving some overhang on the sides for easy removal later.
In a mixing bowl, combine the melted butter, graham cracker crumbs, and 1/4 cup of sugar. Mix until the crumbs are completely coated and the mixture resembles wet sand. Press this mixture firmly into the bottom of the prepared pan to form an even layer.
Place the crust in the preheated oven and bake for 8-10 minutes, or until it’s lightly golden. Remove from the oven and allow it to cool slightly while you prepare the filling.
In a large mixing bowl, combine the softened cream cheese and remaining 1/4 cup of sugar. Using an electric mixer, beat until smooth and creamy. Add the peanut butter and vanilla extract, blending until fully incorporated.
Add the eggs, one at a time, mixing on low speed until just combined after each addition. Avoid overmixing to keep the filling light and airy.
Pour the peanut butter filling over the cooled crust, spreading it evenly. Bake in the oven for 25-30 minutes, or until the edges are set and the center has a slight jiggle.
Once baked, remove the bars from the oven and let them cool in the pan. After they reach room temperature, refrigerate for at least 2 hours (or overnight) to set completely.
Once chilled, use the parchment overhang to lift the bars out of the pan. Slice into squares and serve. Enjoy your Peanut Butter Cheesecake Bars!