Preheat your oven to 325°F (163°C). Grease a 9-inch springform pan and wrap the outside with aluminum foil.
In a medium bowl, combine the graham cracker crumbs, melted butter, granulated sugar, and salt. Press into the bottom of the springform pan.
In a large mixing bowl, beat the cream cheese, granulated sugar, and brown sugar until smooth. Add eggs one at a time, mixing well.
Stir in the vanilla extract and vanilla bean paste until fully incorporated.
In a separate bowl, whisk together the sour cream, flour, and salt. Gradually add to the cream cheese mixture.
Fold in the cooled brown butter until evenly distributed.
Pour the cheesecake filling over the crust. Place the pan in a larger baking dish and fill with hot water halfway up the sides.
Bake for 55-65 minutes until edges are set and center is slightly jiggly. Turn off the oven and crack the door, cooling for 1 hour.
Remove from the water bath and refrigerate for at least 4 hours, preferably overnight, before serving.