Preheat the oven to 325°F. Grease a 9-inch springform pan.
In a medium bowl, combine graham cracker crumbs, melted butter, and 1/4 cup sugar. Mix until well combined. Press the mixture firmly into the bottom of the prepared springform pan to form the crust. Bake for 10 minutes, then remove from the oven and let cool.
In a large mixing bowl, beat the browned butter and cream cheese together until smooth and creamy. Add 1 cup of sugar, vanilla extract, and vanilla bean paste, mixing until well combined.
Add the eggs one at a time, mixing well after each addition. Scrape down the sides of the bowl as needed.
Gently fold in the sour cream and flour until just combined. Pour the cheesecake batter over the cooled crust in the springform pan.
Bake for 50-60 minutes, or until the center is set but still slightly jiggly. Turn off the oven and crack the door, letting the cheesecake cool in the oven for 1 hour.
Remove the cheesecake from the oven and let it cool to room temperature. Refrigerate for at least 4 hours, preferably overnight, before serving.