Cobbler is a term often used to describe a baked fruit dessert with a topping - but this is a true cobbler with crunchy biscuit dough dropped on top.
Heat oven to 375 degrees. Cut pears in half lengthwise; remove stem, core with melon baller, and peel. Slice each half lengthwise into 6 1/2-inch-thick slices and place in a large bowl. Add blackberries, lemon juice, 1/2 cup plus 2 tablespoons granulated sugar, cornstarch, and brandy. Toss gently to combine and transfer to a 3 1/2-quart baking dish.
In a large bowl, whisk together flour, brown sugar, salt, baking powder, and cinnamon. Using two knives, cut the pieces of butter into flour mixture until it resembles coarse meal. Add the milk and stir with a fork until the dough just comes together. Do not overmix.
Drop 1/3 cup dough onto the fruit, and repeat, covering the surface of the fruit with "biscuits" that are just touching. Sprinkle the top with remaining 3 teaspoons granulated sugar and bake until golden brown and juices are bubbling rapidly, about 1 hour. Remove from oven and let cool slightly on a wire rack. Serve with cold heavy cream on the side.