Preheat oven to 325 degrees F for lightly colored pans or 300 degrees F for dark colored pans.
For the crust: In a small bowl, toss crumbs with melted butter. Press onto bottom of 9-inch springform pan. Bake for 8 minutes. Set aside.
For the filling: Meanwhile, combine cream cheese and sugar until well blended. Stir in peach schnapps until just blended. Add eggs, 1 at a time, stirring after each addition until just blended.
Pour onto crust.
Using heavy duty foil, wrap outsides and bottom of pan. Place cheesecake on a wire rack inside a larger pan. Fill larger pan with very hot water 1/3 the way up the springform pan. Bake for 45 to 50 minutes or until center is almost set. Remove cheesecake from hot water bath and remove foil. Let stand 10 minutes before running knife around the edge to loosen cake from sides. Cool for 1 hour then refrigerate uncovered at least 4 hours or overnight.
Just before serving: Remove cake from icebox and remove the sides of the pan. Transfer cheesecake to serving plate. While preparing the topping, allow cheesecake to come to room temperature.
For the topping: In a large skillet, melt butter over medium-high heat. Add brown sugar and allow mixture to caramelize. Add peaches, cook for 3 to 4 minutes or until peaches are well coated and tender. Add brandy and ignite to flambe the peaches. Serve immediately over slice of cheesecake and garnish with walnuts, if desired.