Brown the butter over medium heat until nutty and fragrant. Pour it into a bowl to cool slightly while you prepare the crust.
Combine cookie crumbs, chopped pecans, brown sugar, and half the brown butter. Press evenly into a springform pan and bake for 10 minutes.
Beat cream cheese until smooth, then mix in sugars, sour cream, and remaining brown butter. Add eggs one at a time, followed by vanilla bean and lemon juice.
Pour filling over the crust and place the pan in a water bath. Bake at 325°F (160°C) for about 60–70 minutes until edges are set but center jiggles slightly.
Remove from the oven, cool for 1 hour, then refrigerate at least 6 hours or overnight for the best texture.