Preheat the oven to 350°F.
Put the peaches in a 9-by-9 (or similar) baking pan. Arrange the peaches in a fairly even layer and pat them down.
Sprinkle the top with the zest of lemon, then drizzle all over with the lemon juice.
In the bowl of a stand mixer with the paddle attachment, cream the butter and 3/4 cup of the sugar on medium speed until combined but sandy, about one minute. Add the flour, baking powder, and salt, and beat again until all the flour is incorporated and the mixture is crumbly.
On low speed, slowly add in the milk. Increase the speed to medium and beat until light and fluffy, about two minutes.
Spoon the batter in large scoops over the top of the peaches. With an offset spatula or butter knife, carefully spread the batter evenly over the fruit, no more than 1/2 inch thick in any one place.
Sprinkle the remaining 1/4 cup sugar over the batter. Drizzle the hot water evenly over the sugar, melting the sugar into the topping. Be sure to use all the hot water.
Bake the cobbler for 50 to 60 minutes, or until the top is browned and cracked. A toothpick inserted into the topping should come out dry.
Let the cobbler sit for about an hour to firm up before serving. Serve alone, or with ice cream or yogurt, or with heavy cream poured on top (optional).