In a large saucepan, stir together 1 1/3 cups sugar, the cornstarch, salt and cinnamon. Add water and stir till sugar is mostly dissolved. Add blackberries, blueberries, lemon juice and butter. Cook, stirring frequently, till thickened and bubbly.
Meanwhile, split each biscuit horizontally into thirds. Arrange 16 of the biscuit pieces in the bottom of a lightly greased 8x8x2-inch baking dish (2-quart square), gently pressing pieces together.
Pour the hot berry mixture over the split biscuits. Arrange the remaining 8 or 14 biscuit pieces on top of the berry mixture. Brush biscuit tops lightly with the milk and sprinkle with the 1 tablespoon sugar.
Bake the cobbler in a 400 degree F. oven for 15 to 18 minutes or till biscuits are golden brown. Cool about 45 minutes before serving. Serve the dessert warm with a scoop of ice cream, if you like.