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1. Preheat your oven to 350°F (175°C).
2. In a medium mixing bowl, combine graham cracker crumbs, melted butter, granulated sugar, and vanilla extract. Mix until the crumbs are well coated and resemble wet sand.
3. Press the mixture firmly into the bottom of a 9-inch springform pan, packing it tightly and evenly.
4. Bake for about 10 minutes, or until lightly golden. Remove from the oven and let cool.
5. In a small saucepan, melt ½ cup of unsalted butter over medium heat, stirring occasionally.
6. Continue cooking until the butter turns golden brown and develops a nutty aroma (about 5-7 minutes). Be careful not to burn it!
7. Remove from heat and let cool slightly.
8. In a large mixing bowl, beat the softened cream cheese with an electric mixer on medium speed until smooth (about 2-3 minutes).
9. Gradually add granulated sugar, mixing until well combined. Scrape down the sides of the bowl as needed.
10. Add sour cream, heavy cream, vanilla bean paste, vanilla extract, and salt. Beat on low speed until incorporated.
11. Add eggs one at a time, mixing on low speed after each addition until just combined. Avoid overmixing.
12. Pour in the warm brown butter and mix until just combined.
13. Pour the cheesecake filling over the cooled crust in the springform pan, spreading it evenly.
14. To prevent cracks, wrap the outside of the springform pan with aluminum foil. Place it in a larger baking dish and fill with hot water until it reaches halfway up the sides of the pan.
15. Bake for 55-65 minutes, or until the edges are set but the center has a slight jiggle.
16. Turn off the oven and crack the door open. Let the cheesecake cool in the oven for about 1 hour.
17. After an hour, remove the cheesecake from the oven and the water bath. Let it cool to room temperature on a wire rack.
18. Once cooled, refrigerate for at least 4 hours or overnight before serving.

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