Preheat oven to 350°F. Line the bottom of a 9-inch springform pan with parchment paper and gently spray with nonstick spray. Set aside.
To make the crust, whisk the graham cracker crumbs and sugar together in a medium-sized bowl. Add in the butter and stir until the mixture resembles wet sand. Press the crust mixture into the bottom of the springform pan in an even layer.
2¾ cups graham cracker crumbs, ⅓ cup granulated sugar, 9 tablespoons unsalted butter
Place the pan into the oven to bake for 15 minutes. Once baked, remove from the oven and place onto a cooling rack to cool slightly as you make the cheesecake batter. Increase the oven heat to 400°F
Place the cream cheese and sugar into the bowl of a stand mixer fitted with a paddle attachment. Beat together on high speed for 2 minutes to ensure that the mixture is creamy and that no lumps of cream cheese remain.
24 ounces cream cheese, 10 tablespoons granulated sugar
Add in the heavy cream, sour cream, lime juice, vanilla bean paste, and salt, and mix until fully incorporated, about 30 seconds.
⅔ cup heavy cream, ⅓ cup sour cream, 1½ tablespoons lime juice, 1½ teaspoons vanilla bean paste, 1 teaspoon kosher salt
Mix in the eggs until combined, then add in the cornstarch and mix until combined.
4 large eggs, 2 tablespoons cornstarch
Pour the batter into the springform pan onto the crust. Smooth the top out as well as possible.
Wrap the bottom and up the sides of the springform pan with aluminum foil to prevent any water from seeping in. Place the springform pan into a larger baking pan or broiler pan. Fill the broiler pan with 1 inch of water to create a water bath. Place the pans into the oven to bake for 15 minutes. Reduce the heat to 250°F and bake for 1 hour and 10 minutes.
Once baked, turn the heat off and leave the cheesecake in the oven to cool for 30 minutes with the door closed. Open the oven door slightly and let the cheesecake continue to chill for 30 minutes. Remove the cheesecake from the oven and unwrap the tin foil. Place the springform pan onto a cooling rack to finish cooling completely.
Once cooled, cover with aluminum foil and place it into the fridge to chill for at least 8 hours.
Once the cheesecake has chilled, run a butter knife around the inside edge of the springform pan to release the cheesecake from the pan. Release the springform and remove the sides from the cheesecake. Place the cheesecake onto a cake stand or serving platter.
Spread the sugar topping over the surface of the cheesecake in an even layer. Use a kitchen torch to toast the sugar. Using medium-to-low heat, hold the torch 1 inch away from the sugar and slowly toast the sugar. Once the sugar starts to bubble, move on to another section, as it will burn easily.
⅓ cup granulated sugar
Once all of the sugar is toasted, let it set for several minutes to cool completely before slicing and serving.