Heat the oven to 350°F. Spray and line a 7-inch springform pan with parchment paper. Stir together the graham cracker crumbs, 2 tablespoons granulated sugar, brown sugar and pinch of salt. Mix in the melted 1/2 cup butter. Press across the bottom and up the sides of the pan.

Set the pan on a baking sheet and bake for 8 to 10 minutes. Remove it and let the crust cool.

In a saucepan, lightly stir the 1 1/2 cups sugar and 1/4 cup water together, then heat over medium-high without stirring. Swirl the pan occasionally if needed. When the syrup turns deep amber, remove it from the heat. Whisk in the room-temperature 6 tablespoons butter, then the heavy cream and 3/4 teaspoon salt. Let the caramel cool for 10 to 15 minutes.

Reduce the oven to 325°F. Put a rimmed pan on the bottom rack and set water to boil. Beat the cream cheese, then mix in the 1/2 cup sugar and cornstarch just until combined. Mix in the eggs one at a time and then the vanilla. Stir in the sour cream with a spatula.

Spread half the filling in the cooled crust, add about half the salted caramel, then cover with the remaining filling. Reserve the rest of the caramel for serving. Pour the boiling water into the rimmed pan and set the cheesecake, on its baking sheet, on the rack directly above it. Bake at 325°F for 45 to 50 minutes, until the center is slightly wobbly and the top is barely browned. Check the egg-containing filling with a food thermometer for 160°F.

Turn off the oven and leave its door slightly open with the cheesecake inside for 1 hour. Remove the cheesecake and let it cool toward room temperature for up to another hour. Refrigerate it within 2 hours of finishing baking. Cover and chill for at least 5 hours.

Top the chilled cheesecake with the reserved caramel. If you like, add a sprinkling of salt before serving.