In a medium saucepan combine 1 ½ cups fresh strawberries, and 3 tablespoons granulated sugar Cook on medium-low until the strawberries release their juices.
In a small bowl combine the 3 teaspoons water and 1 ½ teaspoons cornstarch until it makes a slurry and add it to the strawberries. Continue to cook for about 5 minutes until it thickens. Remove from heat.
Cream Cheese Filling
Beat the 1 (8-ounce) package cream cheese until it is smooth. Add the ¼ cup granulated sugar, and 1 large egg until it is combined. Set aside.
Cake
Preheat the oven to 350 degrees Fahrenheit. Spray a 9-inch springform pan with non-stick cooking spray.
Combine 2 cups all-purpose flour and ¾ cup sugar in a large bowl. Add the ½ cup butter pieces and cut into the flour mixture using a pastry cutter or two forks. Mix until it resembles coarse crumbs. Measure ¾ cup of the mixture and set aside to use for the crumb topping.
Add ½ teaspoon baking soda, ½ teaspoon baking powder, and ¼ teaspoon salt to the remaining flour mixture.
In a separate bowl, beat ¾ cup sour cream, 1 large egg, and 1 teaspoon vanilla extract until it is well blended. Gently stir this into the flour mixture until incorporated. The dough will be lumpy and thick.
Assembly
Spread the batter into the bottom of the prepared pan. Spread the batter 1 inch up the sides of the pan. Pour the cream cheese mixture into the center of the pan. Spread until it is about 1 inch from the sides of the pan.
Spread the strawberry filling on top of the cream cheese layer. Sprinkle the ¾ cup reserved crumbs on top.
Bake for for 50-55 minutes. Cool in the pan on a wire rack for about 20 minutes before serving.