Mix 2 tablespoons butter and brown sugar together in a 9-inch round cake pan until blended; spread mixture to evenly cover bottom of pan. Top with pineapple slices; place 1 cherry in the center of each slice.
Combine graham cracker crumbs, 3 tablespoons white sugar, and remaining 3 tablespoons butter in a small bowl; mix well. Press over pineapple slices.
Beat cream cheese and 3/4 cup white sugar in a bowl until blended. Add sour cream and vanilla extract; mix well. Add eggs, 1 at a time; mix on low speed after each addition until blended. Pour into cake pan.
Bake in the preheated oven until the center is almost set, 55 minutes to 1 hour.
Run a knife around the inside edge of pan to loosen cake. Allow to cool completely, about 30 minutes. Invert onto a serving plate; remove pan. Refrigerate for at least 3 hours.