Preheat oven to 350ºF.
To make the crust: Cream together the butter and sugar in a stand mixer fitted with a paddle attachment. Add flour and salt and mix on low until just combined.
Turn the dough out onto a floured surface and gently knead into the shape of a ball. Transfer the dough ball to a quarter-sheet pan; press it out evenly to the edges of the pan. Chill in the refrigerator for at least half an hour before baking. Bake for 15 to 18 minutes, or until the crust is very lightly browned. Let cool.
To make the filling: In a large mixing bowl, whisk together eggs, sugar, lemon zest, lemon juice, and strawberry purée. Add flour and continue mixing until smooth. Pour filling into the cooled crust and bake for 30 to 33 minutes, or until the filling is set. Let cool completely.
Cut into squares and garnish with powdered sugar, sliced strawberries, and lemon zest.