Preheat oven to 325 degrees Fahrenheit and line an 8x8 inch baking pan with parchment paper.
Combine graham cracker crumbs, 1/4 cup sugar, and melted butter in a bowl. Press firmly into the bottom of the prepared pan.
Bake the crust for 10 minutes, then remove and allow to cool slightly.
In a blender, puree strawberries with 2 tablespoons sugar and cornstarch until smooth. Transfer to a small saucepan and simmer over medium heat for 3-5 minutes until thickened, then cool.
In a large bowl, beat softened cream cheese and 1/2 cup sugar until smooth. Add eggs one at a time, followed by sour cream and vanilla extract, mixing until just combined.
Pour the cheesecake filling over the crust.
Drop small spoonfuls of the strawberry sauce onto the filling and use a knife or toothpick to swirl them together.
Bake for 35-40 minutes until the edges are set but the center still slightly jiggles.
Allow to cool to room temperature, then refrigerate for at least 4 hours before slicing into bars.