Step 1: Preheat your oven to 325°F (160°C). Lightly grease the bottom and sides of a 9-inch springform pan. (Optional: trace the bottom onto parchment paper and put a circle in the bottom).
Step 2: In a medium bowl, combine the graham cracker crumbs, sugar, and melted butter for the crust. Stir until it looks like wet sand. Pour into the prepared springform pan and press down firmly into an even layer on the bottom using the bottom of a glass or flat measuring cup. Bake for 10 minutes. Remove and let cool completely on a wire rack.
Step 3: While the crust cools, make the strawberry layer. In a small saucepan, combine the strawberry puree, sugar, cornstarch, and lemon juice. Cook over medium heat, stirring constantly, until the mixture thickens like jam (about 5-7 minutes). Remove from heat, transfer to a small bowl, and let cool completely.
Step 4: Prepare the cheesecake filling. In a large bowl (or stand mixer), beat the softened cream cheese and the ¾ cup granulated sugar until smooth. Beat in the vanilla extract and 1 tsp lemon juice. Stir in the sour cream until fully combined and silky smooth. Add the eggs one at a time, mixing on low speed just until incorporated.
Step 5: Assemble the layers. Pour about half of the cheesecake filling over the cooled crust. Carefully spoon dollops of the cooled strawberry mixture evenly over this layer. Pour the remaining cheesecake filling over the strawberry layer. Gently swirl the layers with a knife or toothpick, being careful not to reach the crust.
Step 6: Carefully place the springform pan in the preheated oven. Bake for 50-60 minutes, until the edges are set but the center is still slightly jiggly. Turn off the oven, prop the door open slightly, and leave the cheesecake inside for an additional hour to cool slowly.
Step 7: Remove the cheesecake from the oven and let it cool completely on a wire rack at room temperature (couple of hours). Cover loosely with plastic wrap and transfer to the refrigerator to chill for at least 4 hours, but preferably overnight, to set properly.
Step 8: While the cheesecake chills, make the crunch topping. In a medium bowl, combine the crushed freeze-dried strawberries, graham cracker crumbs, melted butter, and ¼ cup sugar. Mix until crumbly.
Step 9: Once the cheesecake is chilled and set, carefully remove the sides of the springform pan. Sprinkle the strawberry crunch topping evenly over the top.
Step 10: If desired, melt the white chocolate chips. Drizzle the melted white chocolate over the crunch topping using a spoon or piping bag. Slice and serve.