Make the caramel sauce.
In a heavy-bottomed saucepan over medium heat, melt the sugar, stirring until it becomes smooth and deep amber in color. Remove from the heat and whisk in the cubed butter. Slowly pour in the warm heavy cream while whisking carefully. Stir in the vanilla extract and salt, if using. Let the caramel cool completely.

Prepare the crust.
In a bowl, mix the graham cracker crumbs, sugar, and melted butter until evenly moistened. Press the mixture firmly into the bottom of a 9-inch springform pan. Chill while you prepare the filling.

Make the filling.
In a large mixing bowl, beat the softened cream cheese, sugar, and vanilla extract until smooth and creamy.

Whip the cream.
In a separate cold bowl, whip the heavy cream to stiff peaks.

Fold the filling.
Gently fold the whipped cream into the cream cheese mixture in three additions until light and fluffy.

Add the caramel.
Fold in 1/2 cup of the cooled caramel sauce just until lightly marbled.

Assemble the cheesecake.
Spread the filling evenly over the chilled crust and smooth the top.

Chill.
Refrigerate for at least 5 hours, preferably overnight, until fully set.

Finish and serve.
Drizzle with extra caramel sauce before serving. Slice with a warm knife for clean cuts.