Preheat your oven to 325°F (163°C). Grease a 9x13-inch baking pan or line it with parchment paper for easy removal.
In a medium bowl, combine the graham cracker crumbs, 1/2 cup sugar, and melted butter. Mix until the crumbs are evenly coated. Press the mixture firmly into the bottom of the prepared baking pan to form the crust.
In a large mixing bowl, beat the softened cream cheese with an electric mixer on medium speed until smooth and creamy. Gradually add 1 cup of sugar and continue to beat until well combined.
Add the vanilla extract and mix in the eggs one at a time, ensuring each egg is fully incorporated before adding the next. Scrape down the sides of the bowl as necessary.
Stir in the sour cream, flour, and salt until just combined. Pour the cream cheese mixture over the crust in the baking pan, spreading it evenly.
Bake in the preheated oven for 45-50 minutes, or until the edges are set and the center is slightly jiggly. Turn off the oven and leave the cheesecake bars inside for an additional hour to cool gradually.
Remove from the oven and let cool to room temperature. Once cooled, refrigerate for at least 4 hours or overnight for best results. Cut into squares before serving.