Let the cream cheese sit at room temperature until softened, about 45 minutes. Trim and thinly slice the strawberries.
Melt the butter in the microwave in 20-second bursts until mostly melted, about 40 seconds. Let it cool slightly.
Break the graham crackers into pieces and place them in a food processor. Add the granulated sugar and 1/4 teaspoon kosher salt. Process until fine crumbs form. Add the melted butter and pulse to combine.
Press the mixture into an even layer in an 8x8-inch baking dish, reaching the edges and corners.
Layer enough sliced strawberries on the crust to cover it. Dice the remaining strawberries and refrigerate them for garnish. Refrigerate the crust while you prepare the filling.
In a stand mixer, beat the cream cheese, 1/2 cup powdered sugar, vanilla extract, and remaining kosher salt until light and fluffy, about 3 minutes.
In a separate bowl, whip the heavy cream and remaining powdered sugar until stiff peaks form. Fold half of the whipped cream into the cream cheese mixture. Cover and refrigerate the remaining whipped cream.
Spread half of the cream cheese mixture over the strawberries in an even layer.
Fold the powdered strawberry gelatin into the remaining cream cheese mixture until well combined. Spread this mixture over the cream cheese layer.
Top with the remaining whipped cream, spreading it evenly. Cover and refrigerate for at least 1 hour or overnight.
Garnish with the chopped strawberries before serving. Cut into 9 squares, wiping the knife between each cut for cleaner servings, and serve cold.