Preheat the oven to 375° F.

Peel, halve, and pit the peaches. Slice each half into 3 or 4 wedges.

Combine the peaches, ¼ cup of the sugar, and the cornstarch in a large mixing bowl. Let the fruit stand, stirring occasionally, until the sugar dissolves, 5 to 7 minutes.

Make the dough: Cream together the butter and remaining ½ cup sugar in a medium mixing bowl with a wooden spoon or an electric mixer until smooth. Beat in the egg, vanilla, and lemon zest until the batter is smooth, scraping down the sides of the bowl once or twice as necessary.

Add the flour, baking powder, and salt and stir until just combined.

Transfer the peaches to an 8-inch square-baking pan. Drop the dough in rounded tablespoonfuls over the fruit.

Bake until the fruit is bubbling and the crust is golden, 50 to 55 minutes. Let the cobbler cool slightly and serve it warm.