Heat oven to 350 degrees. In a large bowl, gently mix berries with ¾ cup sugar and lime juice.
In a separate large bowl, combine flour, remaining sugar, cornstarch, baking powder, and salt. Add butter and mix with hands until a crumbly mixture forms. Slowly incorporate cream until the mixture just comes together.
Pour the berry mixture into a 9x11-inch baking dish. Top the berries with spoonfuls of batter, leaving ¼ inch between spoonfuls. Place in oven and bake 35 minutes, or until golden brown on top. Let cool 10 minutes, then serve.