Preheat your oven to 325°F (163°C). In a mixing bowl, combine the graham cracker crumbs, melted unsalted butter, and brown sugar until well blended. Press the mixture firmly into the bottom of a 9-inch springform pan to create an even crust. Bake this crust for about 10 minutes until lightly golden, then remove it from the oven and allow it to cool while you prepare the filling.

In a saucepan over medium heat, melt the unsalted butter for the filling, swirling occasionally. Continue heating until the butter turns golden brown and emits a nutty aroma, about 5-7 minutes. Remove from heat and let it cool slightly.

In a large mixing bowl, beat the softened cream cheese with granulated sugar until smooth and creamy, about 3-4 minutes. Incorporate the vanilla bean paste, blending well. Gradually add in the eggs, mixing on low speed just until combined. Stir in sour cream and brown butter until the filling is smooth and creamy.

Pour the filling over your cooled crust, smoothing the top with a spatula. Bake for 55-65 minutes until the edges are set and the center is slightly jiggly.

Turn off the oven and leave the cheesecake inside for 1 hour. Once the hour is up, remove from the oven and let it cool at room temperature. Refrigerate for at least 4 hours, or overnight for the best flavor before serving.