Place 2 (8-ounce) packages cream cheese in the bowl of a stand mixer (or a large bowl if using an electric hand mixer). Let sit at room temperature until softened, about 45 minutes.
Trim 1 pound strawberries and thinly slice lengthwise.
Melt 1 stick unsalted butter in a small microwave-safe bowl in 20-second bursts until mostly melted, about 40 seconds total (it will melt completely as it sits). (Alternatively, melt the butter in a small saucepan over medium heat.) Set aside to cool slightly.
Break 12 whole graham cracker sheets into rough pieces and place in a food processor fitted with a blade attachment. Add 2 tablespoons granulated sugar and 1/4 teaspoon of the kosher salt. Process until the crackers are the texture of sand, about 15 seconds. Add the melted butter and pulse to combine, 6 to 8 (1-second) pulses. (If using graham cracker crumbs, just stir the crumbs and butter together in a medium bowl.)
Transfer the mixture to an 8×8-inch baking dish. Use the bottom of a measuring cup or your fingers to press the crumbs into an even layer, making sure to reach the edges and fill the corners.
Place enough of the strawberries onto the crust to form a single, even layer. Dice the remaining strawberries and refrigerate in a covered container for garnish. Refrigerate the crust uncovered while you prepare the filling.
Add 1/2 cup of the powdered sugar, 2 teaspoons vanilla extract, and the remaining 1/4 teaspoon kosher salt to the cream cheese. Beat with the paddle attachment on medium speed until light and very fluffy, about 3 minutes.
Place 2 cups cold heavy cream and the remaining 1/4 cup powdered sugar in a second large bowl. (If using a stand mixer, transfer the cream cheese mixture to a large bowl. Wash and dry the bowl and use it to whip the cream.) Beat with the whisk attachment on high speed until stiff peaks form, 2 to 5 minutes. Add half of the whipped cream (about 2 cups) to the cream cheese mixture and gently fold together with a flexible spatula. Cover the remaining whipped cream and refrigerate until ready to use.
Dollop half of the cream cheese mixture (about 2 cups) into the baking dish and spread over the strawberries in an even layer.
Add 1/4 cup powdered strawberry gelatin to the remaining cream cheese mixture. Use a flexible spatula to fold into the mixture until well-combined and no streaks remain. Dollop over the cream cheese mixture and spread into an even layer.
Spoon the remaining whipped cream over the strawberry cream cheese layer and spread into an even layer. Cover and refrigerate for at least 1 hour or up to overnight.
When ready to serve, garnish with the chopped strawberries. Cut into 9 squares, wiping the knife between each cut for cleaner servings, and serve cold.