Heat oven to 350°F (175°C). Line a rimmed baking sheet with foil, to catch drips, or regret it later.
Prepare the peaches: Place the peaches in a 9×13-inch baking pan and in roughly an even layer. Using a zester or a Microplane, finely zest the lemon evenly over the peaches and then squeeze the lemon juice evenly over the peaches, too, catching any seeds before they fall in.
Make the batter: With an electric mixer, beat butter and ¾ of the sugar until sandy, about 1 minute. Add the flour, baking powder and salt and beat until combined, about 30 seconds, then lower the speed and slowly mix in milk. Continue beating at a medium speed for 2 minutes more, until light and fluffy-ish.
Assemble cobbler: Plop the batter in large blobs over the peaches. Carefully spread the batter evenly over the fruit so that it’s no more than ½-inch thick in any place. Sprinkle with remaining sugar and drizzle the hot water evenly over the sugar.
Bake cobbler: Place the baking dish on the foil-lined baking sheet and bake for 60 to 70 minutes, until the top is cracked and golden brown, and a toothpick inserted into the topping comes out batter-free. (It’s best to start checking it at 60 minutes.)
Be patient: Let the cobbler sit in the baking dish on a wire rack for at least 30 minutes before serving, which will give the peach juices a chance to slightly thicken up. To serve, scoop into bowls and drizzle with heavy cream.
