Preheat your oven to 325°F (163°C). In a medium bowl, combine the graham cracker crumbs, 1/4 cup sugar, and melted butter. Stir until the mixture resembles wet sand. Press this mixture firmly into the bottom of your 9-inch springform pan to create an even crust layer. Bake for 8 minutes, then remove and set aside to cool slightly.
In a large mixing bowl, beat the softened cream cheese with 1 cup of sugar until smooth and creamy using an electric mixer. Add the vanilla extract and then incorporate the eggs one at a time, mixing just until combined after each addition. Be careful not to overmix to avoid cracks later.
Pour half of the cheesecake filling over the pre-baked crust and spread evenly. Spoon dollops of the prepared brownie batter over the cheesecake layer, then gently swirl it into the filling with a knife or skewer to create a marbled effect. Pour the remaining cheesecake filling over the swirled brownie layer and smooth the top.
Place the springform pan on a baking sheet to catch any drips. Bake at 325°F (163°C) for 50-60 minutes, or until the edges are set but the center still jiggles slightly when you gently shake the pan. Turn off the oven, crack the door open, and let the cheesecake cool inside for 1 hour to prevent cracking.
Once cooled, drizzle the caramel sauce evenly over the top of the cheesecake. Sprinkle with chopped nuts if using, adding a delightful crunch and a nutty aroma.
Refrigerate the cheesecake for at least 4 hours or preferably overnight to fully set and develop flavors. Before serving, top with a generous dollop of whipped cream for a light, fluffy contrast. Slice with a hot knife for clean pieces.