Peel and pit the peaches, and slice each into eight wedge-shaped slices. In a baking dish, toss with the other ingredients through the cornstarch. Cover the dish with foil and bake at 400 degrees for 12-15 minutes, until the peaches are soft and have thrown off some juice.
While the peaches are in the oven, cut the butter into the flour, and whisk until the butter disappears into crumbs. Whisk in the sugar.
Add the milk and stir lightly with a kitchen fork. Use a rubber spatula to scrape down the sides of the bowl until no dry flour remains. (Add a little more milk if necessary.)
When the peaches come out of the oven, use one teaspoon to scoop up the dough, and another to push it into the peaches. When all the dough is in the baking dish, stir the contents until the peaches and dough pieces are evenly distributed. Sprinkle the brown sugar and cinnamon over the top.
Return the baking dish to the oven and bake, uncovered, for about 30 minutes, or until the tops of the dough are browned. Remove and cool until just warm. Serve in bowls.