Preheat the oven to 325°F. Grease a 9-inch springform pan and wrap the outside with aluminum foil.
In a medium bowl, combine the graham cracker crumbs, melted butter, sugar, and salt. Press into the bottom of the pan.
Bake the crust for 10 minutes, then let it cool.
In a large bowl, beat the cream cheese until smooth. Gradually add sugar, mixing well.
Add vanilla extract and scraped vanilla bean seeds, mixing until incorporated.
Add eggs one at a time, mixing on low speed after each addition.
Gently fold in sour cream, flour, and salt until smooth.
Add brown butter and mix until just combined.
Pour the batter over the cooled crust. Place the pan in a larger baking dish and fill with hot water halfway up the sides.
Bake for 60-70 minutes until edges are set and center is slightly jiggly.
Turn off the oven, crack the door, and let the cheesecake cool for 1 hour.
Cool to room temperature, then refrigerate for at least 4 hours or overnight.