Preheat oven to 325°F (163°C).

Mix crumbs, butter, and sugar; press into a 9-inch springform pan.

Bake for 10 minutes, then cool.

Puree strawberries in a blender.

Strain through a fine-mesh sieve into a small saucepan.

Whisk in sugar and cornstarch; simmer until thickened (about 5 minutes).

Cool completely before using.

Beat cream cheese and sugar until smooth.

Mix in sour cream and vanilla.

Add eggs one at a time, mixing on low speed just until combined.

Pour half the filling over the crust.

Drizzle half the strawberry puree over the filling.

Repeat with remaining filling and puree.

Use a knife or skewer to gently swirl the puree into the filling.

Bake for 55-60 minutes until the edges are set but the center is still slightly jiggly.

Cool in the oven for 1 hour, then refrigerate for at least 6 hours.