Make the crust: In a medium bowl, combine the graham cracker crumbs, brown sugar, and melted butter until thoroughly mixed. Transfer this mixture to a 9-inch or 10-inch springform pan, pressing it firmly into the bottom and slightly up the sides. For the best results, use the bottom of a measuring cup to compact the crust. Freeze for 10-20 minutes while preparing the filling.
Make the filling: Using a hand mixer or stand mixer with a whisk attachment, whip the cold heavy cream on medium-high speed until stiff peaks form, about 4-5 minutes. Set the whipped cream aside.
In another large mixing bowl, beat the softened cream cheese and granulated sugar together on medium speed until the mixture is completely smooth and creamy. Remember to scrape down the sides and bottom of the bowl periodically to ensure even mixing. Add the confectioners’ sugar, sour cream, lemon juice, and vanilla extract, then beat on medium-high speed for 2-3 minutes until the mixture is smooth and fully combined, ensuring there are no lumps remaining.
Gently fold the whipped cream into the cream cheese mixture using a silicone spatula. This process should be done slowly to preserve the airiness of the whipped cream.
Retrieve the crust from the freezer and spread the cheesecake filling evenly over the crust. Smooth the top with an offset spatula. Cover the cheesecake tightly with plastic wrap or aluminum foil and refrigerate for at least 6-8 hours, ideally overnight, to allow it to set properly. For the best results, chill for 12 hours.
Once set, run a knife around the edge of the cheesecake to loosen it from the springform pan, then remove the rim. Slice the cheesecake with a sharp, clean knife, wiping the blade between each cut for neat slices. Serve with your choice of toppings (see Note). Store any leftovers in the refrigerator for up to 5 days.