Beat butter, powdered sugar, and vanilla extract together in a medium bowl until well combined. Add flour and continue to beat until dough comes together and is no longer dry.
Press the dough into an 8×8-inch pan, smoothing the surface evenly with your fingers. Prick the dough all over with a fork to allow any steam to escape.
Bake in the preheated oven until the edges begin to brown, about 20 minutes. Remove from oven and cool completely.
Meanwhile, make the filling. Beat cream cheese, powdered sugar, and vanilla extract together until smooth. Fold in whipped topping until combined. Refrigerate while the shortbread cools and you prepare the strawberry topping.
Whisk water, sugar, and cornstarch together in a small pan over medium heat. Bring to a boil, whisking constantly. Add gelatin and whisk until incorporated. Remove from heat and set aside to cool, whisking occasionally to prevent a skin from forming on the top.
Spread the cream cheese mixture over the cooled shortbread. Top evenly with sliced strawberries then pour gelatin mixture evenly over the strawberries. Refrigerate until set. Cut into squares.