Preheat your oven to 325°F (160°C). In a mixing bowl, combine the graham cracker crumbs, 1/3 cup of granulated sugar, and melted butter until well mixed. Press the mixture evenly into the bottom of a greased 9x9-inch baking pan to form a crust.
In a separate large bowl, beat together the softened cream cheese and powdered sugar until smooth using an electric mixer. Add in the eggs, vanilla extract, and salt, mixing until incorporated.
Gently fold the chopped pecans into the cream cheese mixture until evenly distributed.
Pour the cheesecake mixture over the prepared crust, smoothing the top with a spatula. Drizzle the caramel sauce over the cheesecake layer, and use a knife to swirl it gently into the filling for a marbled effect.
Bake in the preheated oven for 30-35 minutes or until the edges are set and the center is slightly jiggly. Remove from the oven and let cool at room temperature.
Once cooled, refrigerate the cheesecake bars for at least 4 hours or overnight to set completely.
To serve, cut the chilled cheesecake into squares. Drizzle with additional caramel sauce and garnish with pecan halves if desired.