In a bowl, mix the graham cracker crumbs, brown sugar, and melted butter until well blended. Press the mixture firmly into the bottom and up the sides of a 9-inch springform pan.
In a large bowl, beat the softened cream cheese with the granulated sugar until the mixture is smooth. Add the confectioners’ sugar, yogurt, lemon juice, and vanilla extract.
Gently fold the whipped cream into the cream cheese mixture using a spatula. Mix slowly to keep the filling light and airy.
Cover the cheesecake with plastic wrap and refrigerate for at least 6 hours, preferably overnight, until the filling is firm and well set.