Preheat your oven to 350°F (175°C). In a mixing bowl, combine graham cracker crumbs, melted butter, and white sugar until well blended. Press this mixture firmly into a greased 9-inch springform pan to create a sturdy crust. Bake for 8 minutes, then remove from the oven and allow it to cool completely.

In a large mixing bowl, beat the cream cheese with an electric mixer until creamy and smooth. Gradually add both white and brown sugars, mixing until well incorporated. Add the large eggs one at a time, ensuring each egg is fully blended before adding the next. Mix in the sour cream, brewed espresso, and vanilla extract until the filling is thoroughly combined and silky.

Pour the cheesecake filling over the cooled crust, smoothing the top with a spatula. Bake in the oven at 325°F (165°C) for approximately 1 hour and 5 minutes. The center should jiggle slightly but be set around the edges. Once done, turn off the oven and leave the cheesecake inside with the door ajar for 15 minutes to help prevent cracking.

After allowing the cheesecake to cool in the oven, let it rest at room temperature until completely cooled. Transfer it to the refrigerator for at least 8 hours, but overnight is ideal for the best flavor and texture development.

When you're ready to serve, carefully release the sides of the springform pan. Slice the cheesecake into wedges and plate each piece. Top each slice with a generous dollop of fresh whipped cream and drizzle with salted caramel.