Spray a 9 x 13 baking dish with oil and line with parchment.
In a large frying pan, toss the peaches with the sugar, lemon, cinnamon, and zest. Let it rest with intermittent tossing while you make the shortbread.
In a small bowl, lightly beat the egg with the vanilla.
In a large bowl, combine the flour, sugars, and baking powder.
Add the egg mixture into the dry ingredients, mix as well as possible.
Add the diced butter and toss to coat. Treat this as a pastry crust, so use what you are comfortable with: big fork, pastry cutter, fast hands. I like fast hands. Work the mixture rapidly with your hands, trying not to melt the butter, but getting the mixture to a pressable pastry consistency. I would say it took about 5 minutes.
Press half of the mixture into the parchment-lined baking dish and bake for 20 minutes.
While the base is baking, heat the peach mixture to medium. When the mixture comes to temperature, sprinkle the top with the starch, mix well, and reduce the heat. Stir occasionally.
Remove the base from the oven and turn off the heat on the peaches and let them cool to the touch.
Pour and spread the peach mixture on the base. Sprinkle the remaining pastry, as a crumb, over the top of the fruit layer.
Bake, uncovered, for 40 minutes. The fruit should be bubbly and the top crumb a light brown.
Remove from the oven and cool for about an hour on the counter, then transfer to the refrigerator. Cool for an hour. Remove by the parchment to a cutting board and use a sharp, thin knife to slice into 12 squares.
Wrap individually in plastic wrap and store in a container in the refrigerator.