1. Make the Strawberry Sauce:

1. In a small saucepan over medium heat, combine the strawberries, sugar, and lemon juice.
2. Cook, stirring occasionally, until the strawberries soften and release their juices (about 5-7 minutes).
3. Use a potato masher or fork to mash the strawberries into a puree. You can leave some chunks for texture, or puree until completely smooth, depending on your preference.
4. In a small bowl, whisk together the cornstarch and water to create a slurry.
5. Stir the cornstarch slurry into the strawberry puree.
6. Cook for 1-2 minutes, stirring constantly, until the sauce thickens.
7. Remove from heat and let it cool completely. The sauce will thicken further as it cools.
8. Optional: For a smoother sauce, strain the cooled puree through a fine-mesh sieve to remove any seeds or larger pieces.

2. Prepare the Crust:

1. Preheat oven to 325°F (160°C).
2. In a medium bowl, combine the graham cracker crumbs, sugar, and melted butter. Mix well until the crumbs are evenly moistened.
3. Press the crumb mixture firmly and evenly into the bottom of a 9-inch springform pan.
4. Bake for 8-10 minutes, or until the crust is lightly golden and set.
5. Remove from the oven and let it cool while you prepare the filling.

3. Make the Cheesecake Filling:

1. In a large bowl, using an electric mixer (handheld or stand mixer), beat the softened cream cheese and sugar together until smooth and fluffy (about 2-3 minutes).
2. Add the eggs one at a time, beating well after each addition.
3. Add the vanilla extract, sour cream, and heavy cream. Mix on low speed until just combined. Do not overmix.

4. Assemble the Cheesecake:

1. Pour the cheesecake filling over the cooled crust, spreading it evenly.
2. Drop spoonfuls of the cooled strawberry sauce over the surface of the cheesecake filling.
3. Use a knife or skewer to swirl the sauce into the filling, creating a marbled effect. Don’t over-swirl, or the colors will become muddy.

5. Bake the Cheesecake (Water Bath Method):

1. Wrap the bottom of the springform pan tightly with aluminum foil to prevent water from seeping in.
2. Place the springform pan inside a larger baking dish (such as a roasting pan).
3. Carefully pour hot water into the larger baking dish, filling it about 1-2 inches deep. This creates a water bath, which helps the cheesecake bake evenly and prevents cracking.
4. Bake for 55-65 minutes, or until the edges are set and the center still has a slight jiggle when the pan is gently shaken. The internal temperature should reach 150°F (65°C).

6. Cool and Chill:

1. Turn off the oven and crack the oven door open. Let the cheesecake cool in the oven for 1 hour. This gradual cooling helps prevent cracking.
2. Remove the cheesecake from the oven (and the water bath).
3. Let it cool completely to room temperature on a wire rack.
4. Cover the cheesecake with plastic wrap and refrigerate for at least 6 hours, or preferably overnight, to allow it to fully set.

7. Serve:

1. Before serving, run a thin knife or offset spatula around the inside edge of the springform pan to loosen the cheesecake.
2. Carefully release the sides of the springform pan.
3. Slice and serve chilled.
4. Optional: Garnish with additional strawberry sauce, fresh strawberries, or whipped cream.