Preheat oven to 300 degrees F. Line a 9x13-inch baking pan with foil and spray with non-stick cooking spray.
Make the Crust: In a medium bowl, whisk together the graham cracker crumbs, sugar, flour, and salt. Add the melted butter and stir until evenly moistened. Press evenly into the bottom of the prepared pan. Bake until fragrant and beginning to brown around the edges, about 20 minutes. Cool completely.
Make the Filling: In a food processor, process the cream cheese and sugar until smooth, about 3 minutes, scraping down the sides of the bowl as needed. With the processor running, add the eggs, one at a time, until just incorporated, about 30 seconds total. Scrape down the sides of the bowl. Add the vanilla and process to combine, about 10 seconds. Pour the cream cheese mixture over the cooled crust. Bake until the center is almost set but still jiggles slightly when the pan is shaken, about 45 minutes.
Make the Topping: In a clean, dry food processor bowl, process the strawberries and sugar until pureed, about 30 seconds. In a medium bowl, stir the strawberry puree and sour cream together until combined.
Remove the cheesecake from the oven. Pour the strawberry mixture over the cheesecake and gently spread to cover the cheesecake layer completely. Return the pan to the oven and bake until the topping is just set, about 15 minutes.
Transfer the pan to a wire rack and let cool completely, about 2 hours. Refrigerate until cold and set, at least 4 hours or up to 24 hours. Lift the cheesecake out of the pan and cut into squares. Garnish with sliced strawberries, if desired. Store the cheesecake bars in an airtight container in the refrigerator for up to 1 week.