Heat the oven to 350°F. Line the bottom and sides of an 8x8-inch square metal baking pan (about 2 inches tall) with 2 sheets of parchment paper, positioning them perpendicular to each other and making sure they are long enough to hang over all four sides by at least 1 inch to form a sling.

Break 12 whole graham cracker sheets into rough pieces and place in a food processor. Add ¼ cup all-purpose flour, ¼ cup granulated sugar, and ¼ teaspoon kosher salt. Process until the crackers are the texture of sand, about 15 seconds.

Add 1 stick melted unsalted butter and pulse until evenly moistened and starting to clump, 8 to 10 (1-second) pulses. (If using graham cracker crumbs, just stir the crumbs and butter together in a medium bowl.) Reserve ⅔ cup of the mixture for topping.

Transfer the remaining mixture to the baking pan. Use the bottom of a flat measuring cup or your fingers to press the crumbs into an even layer, making sure to reach the edges and fill the corners.

Bake until fragrant and starting to darken around the edges, 12 to 15 minutes. Let cool slightly while you prepare the filling.

Wash and dry the food processor bowl and blade. Process 16 ounces cream cheese in the food processor, scraping down the sides of the bowl as needed, until very smooth and fluffy, 1 to 2 minutes.

Add ½ cup granulated sugar, 1 tablespoon vanilla extract, and ¼ teaspoon kosher salt. Process until combined, about 15 seconds. Scrape down the sides of the bowl. With the motor running, add 2 large eggs one at a time and process, scraping down the sides of the bowl as needed, until just incorporated. Transfer to the graham cracker crust and spread into an even layer.

Cook 12 ounces small diced fresh strawberries and 2 teaspoons cornstarch in a medium saucepan over medium heat, stirring often, until the berries soften and the juices released thicken slightly, 4 to 5 minutes (it’s OK if there’s a film at the bottom of the saucepan). Spoon the strawberries evenly over the cream cheese layer. Sprinkle evenly with the reserved crumb mixture.

Bake until the edges are set and puffed and the center is still slightly jiggly, 30 to 35 minutes. Place the pan on a wire rack and let cool completely, about 2 hours. Cover and refrigerate until chilled, at least 3 hours or up to overnight.

Grasping the excess parchment, lift the slab out of the pan and place on a cutting board. Cut into 12 bars, wiping the knife clean between each cut for the cleanest-looking slices.