Peel the peaches; halve and pit. Place on a cutting board and sprinkle the cut sides with the cinnamon; set aside.
In a small saucepan, bring the maple syrup, salt and water to a simmer over low heat; stir occasionally. (Keep an eye on this so it doesn’t burn; feel free to remove from heat and keep warm if it makes you nervous.)
On a floured surface with a floured rolling pan, gently roll the dough into a 12” x 18” rectangle. Lightly dust as you go with additional flour to keep the dough from sticking (as much as possible!). Cut the dough into 6 squares.
Place a peach half cut side down in the center of one piece of dough. Gently pull the four corners of each piece of dough up and over each peach, pinching the edges to tightly seal.
Repeat with remaining peach halves and pieces of dough. Transfer the dumplings to the prepared dish, forming two rows.