Preheat oven to 350°F. Mix the berries, carrot puree, and 2 tablespoons sugar in an 8 x 12-inch baking dish. Set aside.

Make topping. Place the flour, 4 tablespoons of the sugar, baking powder, and salt in a medium size bowl and mix with a fork. Add the butter and mix in with a pastry cutter, mix until the butter forms pea-size balls. Do not overmix or the butter will melt.

Add the buttermilk and mix with a fork just until the liquid begins to combine with the flour. (There might be some flour that is not mixed in, and the batter will be loose.) Do not over mix.

With a large spoon, dot the top of the berry mixture with the topping mixture.

In a small bowl, stir the remaining 2 tablespoons of the sugar, cinnamon, and cornstarch. Sprinkle evenly over the topping mixture. Drizzle the boiling water over the cobbler and bake until the top is crispy and the topping is cooked through, 30 to 35 minutes.