Preheat your oven to 350 degrees Fahrenheit. Line an 8×8 inch baking pan with parchment paper, leaving an overhang for easy removal.
Prepare the crust: In a medium bowl, combine the flour, sugar, and salt. Cut in the cold butter using a pastry blender or your fingers until the mixture resembles coarse crumbs.
Press the crust mixture evenly into the bottom of the prepared pan. Bake for 15 minutes, or until lightly golden. Let the crust cool slightly while you prepare the filling.
Make the strawberry layer: In a small saucepan, combine the sliced strawberries, cornstarch, and water. Cook over medium heat, stirring constantly, until the mixture thickens, about 3 to 5 minutes. Remove from heat and spread the warm strawberry mixture evenly over the partially baked crust.
Prepare the custard: In a separate bowl, whisk together the instant vanilla pudding mix and cold milk until the mixture thickens, about 2 minutes. Stir in the vanilla extract.
Gently spread the prepared custard mixture over the warm strawberry layer.
Bake the assembled bars for 20 to 25 minutes, or until the custard is set and lightly golden around the edges.
Cool the bars completely on a wire rack. Once cooled, chill in the refrigerator for at least 3 hours before slicing into squares.
Notes
For a firmer crust, chill the dough for 15 minutes before pressing it into the pan.
If you use frozen strawberries, do not thaw them before cooking the filling; the cornstarch will help them break down.
This recipe works well with a graham cracker crust if you prefer a different base flavor.
Slice the bars only after they are fully chilled to get clean cuts.