Preheat your oven to 350°F (175°C). Line the bottom of a 9-inch springform pan with parchment paper and gently spray the sides with nonstick spray.

In a medium-sized bowl, mix together the graham cracker crumbs and brown sugar. Add the melted butter and mix until the mixture resembles wet sand.

Press the crust mixture into the bottom of the springform pan in an even layer. Bake the crust for 15 minutes, then remove from the oven and let it cool while you prepare the cheesecake batter. Increase the oven heat to 400°F (200°C).

In the bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese, granulated sugar, and brown sugar on high speed for 2 minutes until creamy and smooth.

Add the heavy cream, sour cream, salt, and vanilla extract. Beat for 30-45 seconds until fully incorporated.

Beat in the eggs and egg yolk until combined, then add the cornstarch and lime juice. Beat to incorporate.

Pour the cheesecake batter into the prepared springform pan and smooth out the top.

In a medium-sized bowl, whisk together the graham cracker crumbs and brown sugar for the topping. Add the melted butter and mix until the mixture resembles wet sand. Spoon the topping evenly over the cheesecake batter.

Wrap the bottom and sides of the springform pan with aluminum foil to prevent water from seeping in. Place the pan in a larger baking pan or broiler pan and fill with enough warm water to come 1 inch up the sides of the springform pan.

Bake the cheesecake in the preheated oven for 15 minutes. Reduce the heat to 250°F (120°C) and bake for 1 hour.

Turn off the heat and leave the cheesecake in the oven with the door closed for 30 minutes. Crack the oven door and let the cheesecake set for another 30 minutes.

Remove the cheesecake from the oven, unwrap the aluminum foil, and let it cool completely on a cooling rack. Once cooled, cover with aluminum foil and chill in the refrigerator for at least 8 hours, or overnight.