Preheat the oven to 350°F and grease a 10-inch cast-iron skillet or 9x9 baking pan.
To make the dough, cream together the butter and the sugar until smooth then add the vanilla, lime juice, and zest until well blended. Stir in the flour, cornmeal, and salt and blend until smooth.
Take half the dough and evenly pat it into the skillet. Toss the berries with the sugar, cornstarch, lime juice, and zest then place in the skillet. Take the remaining half of the topping and patting it into flat pieces place it over the berries leaving some of the berries exposed. (If you were ambitious, you could also roll out this top portion and cut into shapes, such as stars.)
Bake uncovered for 45-50 minutes or until bubbling and the topping is lightly browned. Allow to cool before serving.