Preheat oven to 300°F. Line a cake pan, with a detachable bottom or springform pan with parchment paper, bottom and sides.
Combine the graham cracker crumbs with brown sugar in a bowl. Add melted butter and stir until all is well combined.
Transfer the mixture into the prepared baking pan and press the crust with a glass, bottom and sides, lifting the crust sides up. Refrigerate the crust while you make the rest.
Prepare the sauce:
Make the strawberry sauce by adding strawberries, sugar, lemon juice, water, cornstarch and vanilla extract in a food blender. Blend until smooth. If you want, you can strain the strawberry sauce to remove any seeds.
Add the sauce to the saucepot and cook until slightly thickened, for 2-3 minutes. Reserve ⅓ cup of the strawberry sauce. Set aside.
Prepare the filling:
Beat the cream cheese and sugar in a bowl until fluffy.
Add condensed milk and sour cream. Beat well.
Then add the eggs, one at a time, beating well after each addition.
Fold in cornstarch and vanilla extract.
Assemble the cake:
Pour half the cream cheese mixture into the prepared crust. Add some of the strawberry sauce on top, in dots (1 tsp), then swirl it around.
Pour the remaining cream cheese on top and add the rest of the strawberry sauce. Make swirls with a chopstick or with the tip of a knife. I added dots and just went through the center of each. This way, I created a heart-shaped swirl.
Bake the cake:
Bake the cake in your preheated oven for 45-50 minutes. The center should still be jiggly. Remove the cake from the oven and set aside to cool. Then, chill the cake overnight in the fridge.
Serve:
Slice the cake and serve it with some extra strawberry sauce on top.
Notes
You can add some lemon zest to the cake filling. I would use around 2 teaspoons.