Melt the butter in a saucepan over medium heat. Once melted, increase to medium-high and cook until it sputters and foams. Pour it into a heatproof bowl, scraping the pan to capture the brown bits, and set aside to cool slightly.

Preheat the oven to 350°F. Grease and line an 8 or 9-inch cake pan with parchment paper. In a bowl, combine ground pecans, cookie crumbs, powdered sugar, and ½ cup plus 1 tablespoon of the browned butter (reserve most brown bits for filling). Press the mixture firmly into the bottom and halfway up the sides of the pan. Bake for 10 minutes and then reduce the temperature to 325°F.

Beat the softened cream cheese, brown sugar, salt, reserved brown bits, and vanilla bean until smooth. Add the sour cream and beat until well combined. Add the eggs and mix until just combined. If there are lumps, strain the filling through a fine mesh sieve.

Fill a 13×9-inch pan halfway with warm water. Place the cheesecake pan in the center and bake for at least 1 hour, or until no longer jiggly in the center and the top appears matte. Turn off the oven, prop the door open with a wooden spoon, and let the cheesecake cool for at least 30 minutes. Refrigerate for a minimum of 8 hours.

In a food processor, blend the heavy cream, vanilla extract, salt, and brown sugar until thickened but not overwhipped. Top the cheesecake with whipped cream and serve.