Preheat oven to 350 degrees. Spray a 9×13 inch dish with cooking spray.

Process graham crackers in a food processor until big crumbs have formed. Stir in melted butter. Press the graham crackers into the bottom of the baking dish. Bake for 10 minutes in the preheated oven.

Beat cream cheese with an electric mixer until lighter. Add 1/3 cup sugar, milk, egg, sour cream, and vanilla and beat until well combined. Pour over baked crust.

In a small sauce pan over medium heat, combine strawberries, lemon juice, and 1/4 cup sugar. Let simmer, stirring occasionally, until strawberries have mostly broken down. Mix cold water and cornstarch together, then add to strawberry mixture. Cook until cornstarch is no longer white and the mixture has thickened. Pour over cheese cake mixture.

Bake the bars in the preheated oven for 20 minutes, or until no longer jiggly.

Let cool for ten minutes before cutting, or you may prefer to refrigerate it for a few hours before serving. Cut into squares to serve.