Preheat the oven to 325°F (160°C).
In a mixing bowl, combine the graham cracker crumbs, melted butter, and ¼ cup sugar. Mix until well combined.
Press the crumb mixture firmly into the bottom of a greased 9x13-inch baking dish to form an even crust. Bake for 10 minutes, then remove from the oven and set aside to cool slightly.
In a separate bowl, using an electric mixer, beat the softened cream cheese until smooth.
Add ½ cup sugar and mix until well combined. Then, add the eggs one at a time, mixing well after each addition.
Mix in the vanilla extract and sour cream until the filling is smooth and creamy.
Pour the cheesecake filling over the cooled crust, spreading it evenly. Bake for 30 minutes or until the center is set but slightly jiggly.
Remove from the oven and let the bars cool at room temperature for about 1 hour, then refrigerate for at least 4 hours or overnight.
Once chilled, use a rubber spatula to gently smooth the surface of the cheesecake bars.
Before serving, sprinkle an even layer of ⅓ cup sugar over the top of the cheesecake. Using a cooking torch, caramelize the sugar until it forms a crispy crust.
Allow the crispy topping to cool and set for a few minutes, then slice into bars and serve.