1. Prepare the Crust:

1. Preheat your oven to 325°F (160°C). Line a 9×9-inch baking pan with parchment paper, leaving an overhang for easy removal.
2. In a bowl, mix graham cracker crumbs, granulated sugar, and melted butter until combined.
3. Press the mixture evenly into the bottom of the prepared pan. Bake for 10 minutes, then set aside to cool slightly.

2. Make the Cheesecake Filling:

1. In a large bowl, beat the softened cream cheese until smooth and creamy.
2. Add the granulated sugar and brown sugar, and beat until combined.
3. Mix in the eggs, one at a time, followed by the vanilla extract and heavy cream.
4. Pour the cheesecake filling over the baked crust, spreading it into an even layer.

3. Bake the Cheesecake Bars:

1. Bake at 325°F (160°C) for 30-35 minutes, or until the center is set but slightly jiggly.
2. Remove from the oven and allow the bars to cool to room temperature, then refrigerate for at least 4 hours, or overnight.

4. Add the Crème Brûlée Topping:

1. Before serving, sprinkle the 1/4 cup granulated sugar evenly over the top of the chilled cheesecake bars.
2. Use a kitchen torch to caramelize the sugar until it forms a golden, glassy crust. (Alternatively, place the pan under a broiler for 1-2 minutes, keeping a close eye to prevent burning.)

5. Slice and Serve:

1. Carefully lift the cheesecake out of the pan using the parchment overhang.
2. Slice into bars with a sharp knife, wiping the blade clean between cuts for neat edges.
3. Serve immediately and enjoy the satisfying crack of the caramelized topping!