Preheat oven to 350 degrees F.
Set butter in an 8-inch square baking dish and set in the oven. Let butter melt completely and get a little brown on the edges, about 8 minutes. Then remove from oven and set aside to cool briefly. Tip the dish carefully to coat all the sides with butter.
Meanwhile, mash strawberries with a fork and toss with ⅓ cup sugar. Set aside.
In a small dish, stir to combine the milk and remaining ⅓ cup sugar.
In a medium bowl, combine the flour, cornmeal, baking powder, and sea salt. Fold wet ingredients into the dry.
Carefully spoon batter into baking dish with hot butter (it may spit a little bit). Smooth out batter as best you can, it will be separate from the butter and that’s ok. Spoon the strawberries and all their juices on top – they should be somewhat evenly distributed over the center of the cake.
Bake 30 - 35 minutes or until a toothpick inserted in the center comes out with just a few crumbs attached.
Cool 30 minutes, then slice and serve with vanilla ice cream.
