Place strawberries, sugar, and lemon juice in a small saucepan over medium heat and cook until the berries soften, about 5–7 minutes.

Use a potato masher or fork to break them into a coarse or smooth puree based on preference.

Stir in the cornstarch slurry and cook 1–2 minutes until thickened, then remove from heat and cool completely; strain if desired.

Preheat the oven to 325°F (160°C).

In a medium bowl mix graham cracker crumbs, ⅓ cup sugar, and melted butter until evenly combined and pack firmly into the bottom of a 9-inch springform pan.

Bake for 8–10 minutes to set the crust, then allow it to cool while you make the filling.

In a large bowl beat softened cream cheese and 1 cup sugar with an electric mixer until smooth and fluffy, about 2–3 minutes.

Add eggs one at a time, mixing gently after each addition to avoid incorporating too much air.

Mix in vanilla, sour cream, and heavy cream until just combined; avoid overmixing.

Pour filling onto the cooled crust and smooth the top.

Drop spoonfuls of cooled strawberry sauce across the surface and use a knife or skewer to create a marbled pattern.

Place the springform pan in a larger baking dish and add 1–2 inches of hot water to the outer dish for a water bath.

Bake for 55–65 minutes until edges are set and center jiggles slightly.

Turn off the oven, crack the door, and let the cheesecake cool in the oven for 1 hour.

Remove from the water bath, cool to room temperature, then refrigerate for at least 6 hours or overnight.