Preheat oven to 350°F and line a 9×13-inch pan with parchment paper.  

Strawberry Mixture

1. In a medium saucepan, whisk together the sugar and cornstarch.  Add 1/2 the strawberries and lemon or lime juice and stir to combine.  Place over low heat.  
2. Mash the berry mixture slightly with a potato masher to help release the juices.  Stir frequently and cook for 5-6 minutes until the strawberries are soft and release their juices. Increase the temperature to medium, stirring constantly, until the strawberry mixture gets thick. It will be very thick.  
3. Once it’s thick, stir in the remaining strawberries and cook for another minute, stirring constantly. Remove from the heat and let cool while you make the crumble. 
4. In a food processor, add the flour, sugar, brown sugar, baking powder, cornstarch, and salt. Pulse 1-2 times, and then add the butter. Pulse until the mixture resembles cookie crumbs. 
5. Whisk the egg and vanilla with a fork in a small bowl.  Add the egg and vanilla mixture to the food processor bowl and pulse until the mixture clings together. If you pinch some of it, it should hold together. 
6. Dump about ⅔ of the mixture into your prepared baking dish. Press it firmly with your hands, the back of a spoon or the bottom of a measuring cup, making it as even and level as possible.
7. Pour the strawberry mixture over the top, spreading evenly.
8. With the remaining crumble, sprinkle it evenly over the top of the strawberry layer. To get a nice-sized crumb with good crunch, I take a handful of mixture and press it together in my hands before I sprinkle it on top. 
9. Bake for about 50-55 minutes, or until the top crumble part is light golden brown. The mixture should gently bubble and lift all the way to the middle.  
10. Remove from the oven and let cool completely before drizzling with icing.

Drizzle

Whisk icing sugar and milk or cream in a small bowl until smooth, and drizzle over cooled cake.