Preheat your oven to 350°F (175°C). Wrap the bottom of a 9-inch springform pan tightly with heavy-duty foil for a water bath.
Prepare the crust: Mix graham cracker crumbs, 1/4 cup sugar, and 6 tablespoons melted butter. Press firmly into the bottom of the prepared pan. Bake for 10 minutes. Set aside to cool slightly.
Prepare the peach layer: In a saucepan, combine peach slices, 1/4 cup brown sugar, 1 teaspoon cinnamon, cornstarch, and water. Cook over medium heat, stirring gently, until the sauce thickens slightly, about 5-7 minutes. Remove from heat and let cool.
Prepare the streusel topping: In a small bowl, combine flour, 1/4 cup brown sugar, and 1/4 teaspoon cinnamon. Cut in the 4 tablespoons of cold, cubed butter using your fingers or a pastry blender until coarse crumbs form. Chill until needed.
Prepare the cheesecake filling: Beat the softened cream cheese with 1 1/2 cups sugar until smooth. Beat in vanilla extract and heavy cream. Add eggs one at a time, mixing just until combined after each addition. Do not overmix.
Assemble the cheesecake: Pour half of the cheesecake batter over the cooled crust. Spoon the cooled peach mixture evenly over the batter. Pour the remaining cheesecake batter over the peaches.
Bake in a water bath: Place the foil-wrapped springform pan into a larger roasting pan. Carefully pour hot water into the roasting pan until it reaches halfway up the sides of the springform pan. Bake for 60-75 minutes, or until the edges are set but the center still has a slight wobble.
Top and finish baking: Carefully remove the pan from the water bath and remove the foil. Sprinkle the chilled streusel topping evenly over the top. Return the cheesecake to the oven (without the water bath) and bake for another 10-15 minutes, until the topping is golden brown.
Cool and chill: Turn off the oven and let the cheesecake cool inside the oven with the door ajar for 1 hour. Remove the cheesecake from the oven, let it cool completely on a wire rack, then cover and refrigerate for at least 6 hours, or preferably overnight, before serving.
Notes
You can prepare the peach layer and the streusel topping one day ahead and store them covered in the refrigerator.
For best results, allow the cheesecake to come to room temperature for about 30 minutes before slicing.
This dessert keeps well, covered, in the refrigerator for up to 4 days.