Grease a 9 x 13 ceramicor glass baking dish with unsalted butter.
In a large bowl, whisk together the 1 tablespoon of cornstarch and ½ cup of cane sugar. Optional: If your fruit is ripe and at the height of the season, no need to add this additional sugar.
Thoroughly wash 2 pounds of peaches, 1 pound of blackberries, and 1 lemon (including the rind) under cool, running, drinkable water.
Slice the peaches into ½-inch wedges. Add the peaches to the large bowl and squeeze 2 tablespoons of lemon juice over the sliced fruit. Stir to combine. Transfer to the baking dish and bake until bubbling, about 15 minutes.
Meanwhile, in a food processor mix together 1¼ cups of all-purpose unbleached flour, ¼ teaspoon of kosher salt, and 1½ teaspoons of baking powder.
Cut 6 tablespoons of chilled unsalted butter into ¼-inch pieces, add to the food processor and pulse in on/off blasts until it resembles coarse meal. Add ⅔ cup of pasteurized whole milk through the top and pulse until dough is just combined.
Remove the baking dish from the oven. Drop the dough onto the fruit mixture in 12 mounds, about⅓ cup each, and sprinkle the dough with the 1 tablespoon of turbinadosugar.
Bake until the cobbler is golden brown, about 30-35 minutes. Serve warm. Eat up, Mama!