Preheat the oven to 375 degrees F.
Add the peaches, 1/2 cup of the sugar, the cornstarch, the lemon zest, and the lemon juice to a medium-sized saucepan over medium heat.
Bring the mixture to a simmer for 5 minutes. Stir continuously until the peaches start to soften.
Take the saucepan off the heat and set it aside.
Place the cubed butter in a 9×9-inch baking dish and put it into the preheated oven until the butter has melted.
Add the flour, baking powder, salt, remaining sugar, egg, vanilla, and milk to a bowl, and whisk until the flour is just combined.
Pour the peaches into the baking dish over the melted butter.
Pour the batter evenly over the peaches.
Bake in the oven until the cobbler is golden brown, about 40-45 minutes.
Serve immediately with some ice cream.