Preheat your oven to 325°F (160°C). Wrap the outside of a 9-inch springform pan tightly with heavy-duty aluminum foil.
Prepare the crust: Combine graham cracker crumbs, 1/4 cup sugar, and melted butter. Press the mixture firmly into the bottom of the prepared springform pan. Bake for 10 minutes. Let cool slightly.
Prepare the cheesecake filling: In a large bowl, beat the softened cream cheese with an electric mixer until smooth. Gradually beat in 1 1/2 cups sugar, vanilla bean paste, and salt until combined.
Beat in the eggs one at a time, mixing just until each egg is incorporated. Mix in the heavy cream until the batter is smooth. Do not overmix.
Pour the filling over the cooled crust. Place the springform pan inside a larger roasting pan. Carefully pour hot water into the roasting pan until it reaches halfway up the sides of the springform pan (this is a water bath).
Bake for 55 to 65 minutes, or until the edges are set but the center still jiggles slightly.
Turn off the oven, crack the door open slightly, and let the cheesecake cool in the oven for 1 hour.
Remove the cheesecake from the water bath and let it cool completely on a wire rack. Once cool, chill in the refrigerator for at least 6 hours, or preferably overnight.
When ready to serve, remove the cheesecake from the pan. Sprinkle an even, thin layer of the remaining 1/2 cup sugar over the top.
Use a kitchen torch to caramelize the sugar until it forms a hard, amber crust. Serve immediately after torching.
Notes
Use vanilla bean paste for the best flavor in the cheesecake filling.
Chill the cheesecake completely before torching the sugar topping for the best texture contrast.
If you do not have a kitchen torch, you can place the sugared cheesecake under a hot broiler for 1-2 minutes, watching constantly to prevent burning.