Preheat oven to 400 degrees F (200 degrees C).
Combine 1/2 cup sugar, cornstarch, and cinnamon in a saucepan and whisk to mix. Stir in sliced peaches (see Editor’s Note) and lemon juice, tossing until peaches are evenly coated.
Cook filling over medium heat, stirring constantly, until mixture thickens and boils. Boil 1 minute. Pour mixture into an ungreased 2-quart casserole dish. Keep mixture hot in oven while you make the topping.
In a medium bowl combine flour, 1 tablespoon sugar, baking powder, and salt. Mix thoroughly, then cut in shortening until mixture looks like fine crumbs. Add milk and stir until mixture is evenly moistened.
Remove peach filling from oven and drop dough onto peaches in 6 equal-size spoonfuls.
Return cobbler to oven and bake until topping is golden brown, 25 to 30 minutes.
To peel peaches, fill a large saucepan with water and bring to a boil. Turn off the heat and add the peaches. Let the fruit sit in the hot water for one minute to loosen the skins. Remove peaches with a slotted spoon and transfer to a bowl of ice water. When peaches are cool enough to handle, slip off the skins and slice.
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