Preheat oven to 350°F (175°C). Grease an 8x8-inch baking pan or line with parchment paper.
Whisk together flour, baking powder, cornstarch, and salt in a bowl. Set aside.
In a large bowl, mix melted butter white sugar, and brown sugar until smooth.
Add eggs, yolk and vanilla extract, lemon juice, lemon extract, water, and lemon zest. Whisk until combined.
Gradually add dry ingredients to wet, and stir until just combined.
Gently fold in diced strawberries.
Pour batter into the prepared pan, and spread evenly. Bake for 35 minutes or until the edges are golden and a toothpick comes out clean.
Mix the icing ingredients in a bowl. Be patient with this. The small amount of liquid combined with the powdered sugar makes the perfect thick icing. Be sure to continue to whisk until the sugar has dissolved. If the icing is too thick, thin it out with a little milk or water.
Cool in pan on a wire rack. Once completely cooled add icing to the top. Slice into squares and serve.