Preheat oven to 375°F (190°C). Grease an 8x8-inch pan with butter and line the pan with parchment paper, leaving an overhang on all sides. Grease the parchment paper with butter, then set it aside.
Make the graham cracker crust: Using a food processor or blender, pulverize the graham crackers into a fine crumb. Pour into a medium bowl and mix with the granulated sugar, melted butter, and salt. Press firmly into the lined pan and bake for 8-10 minutes. Allow to cool as you prepare the filling. And then reduce the oven to 325°F (165°C).
Make the cheesecake filling: Using a handheld or stand mixer fitted with a paddle attachment, beat the cream cheese and granulated sugar together on medium speed in a large bowl until the mixture is smooth and creamy, about 2 to 3 minutes. Add the heavy cream, lemon juice, and vanilla beans (or vanilla bean paste), then beat until fully combined. At low speed, add the eggs one at a time, beating after each addition until just combined. After the final egg is fully incorporated into the batter, stop mixing.
Pour the batter into the slightly cooled crust and firmly tap the pan on a hard surface to release any air bubbles. Check to make sure your oven has cooled to 325°F (165°C), then bake for 35-40 minutes, until the filling is set but still a little jiggly in the center. (An instant-read thermometer, inserted into the filling about 1" in from the edge, should read between 180°-190°F (80°-90°C.) The cheesecake will continue to cook and set as it cools.
Remove the bars from the oven and cool at room temperature for 2 hours. Refrigerate until cold, at least 3 hours but preferably overnight.
Use the parchment paper overhang to lift the cheesecake bars out of the pan and onto a cutting board. Cut into squares, wiping the knife clean with a warm, damp paper towel between slices. Refrigerate until ready to serve.
Leftovers should be stored in an airtight container and kept in the refrigerator for up to 5 days.