Preheat the oven to 350 degrees Fahrenheit. Spray a 9×13-inch baking pan with nonstick cooking spray.
In a medium bowl, toss peach slices with the lemon zest, lemon juice, cornstarch, vanilla extract, and granulated sugar. Spread the peaches across the bottom of the prepared baking pan.
In a large bowl, stir together the flour, powdered sugar, baking powder, and salt. Use a pastry cutter to cut in the butter until it resembles a course meal. (Alternatively, you can pulse the ingredients in a food processor.)
Pour in the half-and-half. Stir to form a thick batter.
Scoop the batter in large clumps on top of the peaches to form a nice cobbler crust.
Bake for 1 hour and then transfer to a wire rack to cool completely. Once cooled, store covered in the refrigerator for up to 5 days.