Preheat the oven to 350°F (180°C), or 160°C for a fan oven. Line a 9×5 inch (approx 23×13 cm) loaf pan with parchment paper.
In a medium bowl, add the flour, cornstarch, baking powder, and salt and whisk to combine; set aside.
In a bowl of a stand mixer, cream the butter and sugar together until light and fluffy. Add the eggs and vanilla and beat again.
Add half the flour mixture, followed by the milk, followed by the remaining flour and mix well.
With a spatula, gently fold in strawberries and lemon zest if using.
Pour batter into prepared loaf pan, and bake in the preheated oven for 50-55 minutes or until a toothpick comes out clean or with a few wet crumbs on it.
Allow to cool completely before icing the cake.
To make the icing, in a medium bowl, combine powdered sugar, mashed strawberries, melted butter and lemon juice. Gently stir until an icing forms.
Place the cake on a wire rack fitted with a sheet pan, and pour the glaze over the top so it drips down the sides. Let it sit for at least 30 minutes before slicing.