Preheat your oven to 350°F and set the oven rack in the middle position.
In a medium bowl, mix the graham cracker crumbs, brown sugar, and melted butter. Press crumbs into the bottom and about ½-inch up a 9-inch springform pan.
Bake for 8-9 minutes until lightly browned, then set aside to cool. Wrap the outside of the pan tightly with 1 or 2 sheets of aluminum foil (to prevent water from seeping into the seams). Reduce the oven temperature to 325°F.
In a large bowl, or stand mixer fitted with the paddle attachment, beat the cream cheese and sugar for about 5 minutes. Stop and scrape the bowl 2-3 times to ensure even mixing and no lumps remain.
Add the eggs one at a time, beating until the mixture is smooth before adding the next egg.
Add the sour cream and vanilla and mix just until smooth.
Pour the batter into the crust and tap it on the counter a few times to remove large air bubbles.
Place a large roasting pan in the oven and fill it with 1 inch of boiling water. Place the cheesecake pan in the water and bake for 75-80 minutes. It's done when the edges are set and the center wobbles slightly when you tap the pan.
Remove the cheesecake from the water and let it cool at room temperature for 2 hours. Then, cover and refrigerate for at least 4 hours.
Nutrition information is calculated using an ingredient database and should be considered an estimate.