Blackberry Farm’s Blackberry Cobbler

8 cups fresh blackberries 

1 1/4 cups sugar 

Zest and juice of 1/2 lime 

1 Tbs. cornstarch 

1 1/4 cups all-purpose flour 

1 1/4 tsp. baking powder 

1/4 tsp. baking soda 

1/8 tsp. fine sea salt 

6 Tbs. (3/4 stick) unsalted butter, cut into small cubes and chilled 

1/4 cup buttermilk