Preheat the oven to 325°F. Lightly grease a 9-inch springform pan and wrap the outside with foil to prevent leaks during the water bath.

In a small saucepan over medium heat, melt the butter and continue cooking until it turns golden brown and smells nutty. Remove from heat and let it cool slightly.

In a medium bowl, combine the graham cracker crumbs, sugar, salt, and browned butter. Mix until the crumbs are evenly coated. Press the mixture firmly into the bottom of the springform pan. Bake for 10 minutes, then remove from the oven and let cool.

In a large bowl, beat the softened cream cheese and sugar until smooth and fluffy. Add the vanilla bean paste and mix until fully incorporated.

Add the eggs one at a time, mixing well after each addition. Scrape down the sides of the bowl to ensure a smooth batter. Blend in the sour cream, heavy cream, and salt until just combined.

Pour the filling over the cooled crust. Tap the pan gently on the counter to release any air bubbles.

Place the cheesecake in a larger baking dish and fill the outer dish with hot water to create a water bath. Bake for 55 to 65 minutes, or until the edges are set and the center has a slight jiggle.

Turn off the oven, crack the door slightly, and let the cheesecake cool inside for 1 hour. Remove from the oven and let it cool to room temperature before chilling in the refrigerator for at least 4 hours or overnight.

For the optional topping, mix the sour cream, powdered sugar, and vanilla extract. Spread over the chilled cheesecake before serving.