Step 1: Preheat your oven to 350°F (175°C). Line a 9x13 inch baking pan with parchment paper, leaving an overhang on the sides to easily lift out the bars later.
Step 2: In a medium bowl, combine the graham cracker crumbs, melted butter, and 1/4 cup granulated sugar. Press the mixture firmly and evenly into the bottom of the prepared baking pan.
Step 3: Bake the crust for 8-10 minutes, or until lightly golden. Remove from oven and let cool slightly while you prepare the filling. Reduce oven temperature to 325°F (160°C).
Step 4: In a large bowl, using an electric mixer, beat the softened cream cheese until smooth and creamy, about 2-3 minutes.
Step 5: Add the sour cream and 1 cup granulated sugar to the cream cheese. Beat on low speed until just combined, scraping down the sides of the bowl as needed.
Step 6: Beat in the eggs one at a time, mixing just until each is incorporated. Stir in the vanilla extract. Be careful not to overmix the batter.
Step 7: Pour the cream cheese filling evenly over the cooled graham cracker crust.
Step 8: Drizzle 1/2 cup of caramel sauce over the cheesecake filling. Using a knife or skewer, gently swirl the caramel into the cheesecake batter to create a marbled effect.
Step 9: Bake for 40-45 minutes, or until the edges are set and the center is slightly jiggly. Do not overbake.
Step 10: Turn off the oven, prop the door open slightly, and let the cheesecake cool in the oven for 1 hour. This helps prevent cracking.
Step 11: Remove from the oven and let cool completely on a wire rack. Once cooled, refrigerate for at least 4 hours, or preferably overnight, before lifting out of the pan and cutting into bars. Drizzle with extra caramel sauce before serving, if desired.