Spray a 9x13" baking dish with cooking spray. Preheat your oven to 350 degrees.
Wash and hull the strawberries. Dice and set aside.
Melt butter in a large bowl. Whisk in the sugars. Add the eggs, lemon juice, and zest and whisk again.
In a separate bowl, whisk together the flour, cornstarch, baking powder, and salt. Add to the wet ingredients and stir a few times.
Gently fold the diced strawberries.
Spread the dough evenly into the prepared baking pan. Bake at 350° for 35-40 minutes, or until light golden brown on top.
For the glaze, finely smash a large strawberry and measure a tablespoon of puree. Whisk together the powdered sugar, zest, salt, puree, and enough lemon juice to make a thin glaze.
Pour the glaze over the warm bars and spread out evenly.
Let the bars cool completely before cutting into squares.
Notes
The strawberries release moisture as the bars sit, so don't underbake them, or they will get soggy.