Combine cornstarch, cinnamon, sugar and water in saucepan. Cook and stir until thickened. Add sliced peaches, lemon juice and butter. Cook just until peaches are hot, about five minutes.
Sift together flour, sugar, baking powder, and salt. Cut in butter until mixture resembles coarse crumbs. Combine milk and beaten egg. Add all at once to dry ingredients, stirring, just to moisten. Pour filling into 9 × 13 inch pan. Top with globs of dough.
Bake at 350° F for 20–25 mininutes. Serve warm with cream or ice cream.