Place the peaches in a large skillet or dutch oven.
In a small bowl combine the cornstarch, sugar and salt; sprinkle over the peaches.
Place dutch oven on a burner over medium heat until it reaches simmering.
Stir occasionally and gently, simmering for ten minutes; remove from heat.
Whisk the flour, sugar, baking soda, baking powder, and salt together in a large bowl.
Add the butter, and combine using a pastry blender (or two forks) until butter is reduced to the size of peas.
Add the milk and vanilla, and stir until just combined.
Divide the dough into eight pieces, and place evenly over peach mixture. Add 1/3 cup water, pouring between dumplings.
Return the pot to the stove, and bring to a low simmer.
Cover fully with a lid, and simmer for about twenty minutes, or until dumplings are puffy and cooked through.
Uncover and let sit for fifteen minutes before serving.
If desired, sprinkle the top of each dumpling with cinnamon and sugar or serve with a dollop of whipped cream