Preheat your oven to 350°F. Crush shortbread cookies into fine crumbs (about 2 cups). Mix crumbs with melted butter, 2 tablespoons sugar, and a pinch of salt. Press firmly into a 9-inch pie dish using the bottom of a flat measuring cup. Bake for 10 minutes until toasted and fragrant. Cool completely on a wire rack.
In a large bowl, beat softened cream cheese until smooth and lump-free. Slowly beat in the sweetened condensed milk, lemon juice, and vanilla. The mixture will thin slightly – that is normal. Pour into cooled crust and spread evenly. Tap gently to release air bubbles.
Place the dish in the freezer, uncovered, and freeze for at least 2 hours until the filling is firm to the touch.
In a medium saucepan, combine quartered strawberries and 1/3 cup sugar. Cook over medium heat, stirring occasionally, until berries release juice and mixture simmers – about 5 minutes.
Stir the cornstarch dissolved in 2 tablespoons cold water into the berries. Cook for 2 more minutes, stirring constantly, until thickened and glossy. Remove from heat and cool completely.
Spoon cooled strawberry mixture over the frozen cream cheese layer and spread evenly. Return to freezer for at least 1 hour until firm.
Whip heavy cream and powdered sugar until soft peaks form. Spread over the frozen strawberry layer.
Cover loosely with plastic wrap or foil and freeze for at least 4 hours, preferably overnight. Slice with a warm knife for clean cuts.