Preheat oven to 350°F. Line the baking sheet with parchment paper.
Wash and hull the strawberries. Cut them into pieces.
For the strawberry topping: Combine the berries with cornstarch, sugar, and a splash of lemon juice in a large bowl.
For the batter: In a separate bowl, cream together the softened butter, sugar, vanilla extract, lemon zest, and salt. Add the eggs one at a time, mixing well after each one is added.
Whisk together the flour and baking powder, then sift it into the butter-egg mixture. Mix until smooth.
Spread the batter evenly onto the prepared baking sheet. Top with the strawberry mixture.
Combine the flour, sugar, salt, and cold butter to make the crumble topping. Sprinkle it evenly over the strawberries.
Bake for about 40 minutes, or until the crumble is golden brown.
Let the cake cool completely before cutting into pieces.
