Instructions

For the dough: Adjust oven rack to middle position and heat oven to 350 degrees. Combine flour, sugar, baking powder, and salt in large bowl. Combine milk and melted butter in second bowl (butter may form clumps). Using rubber spatula, stir milk mixture into flour mixture until just incorporated. Turn out dough onto lightly floured counter and knead until no streaks of flour remain, about 1 minute. Return dough to large bowl, cover with plastic wrap, and set aside.
For the peaches and sauce: Set aside 12 peach slices. (If using frozen peaches, select 12 largest slices and freeze until ready to use.)
Combine water, butter, ⅓ cup sugar, salt, and remaining 4 peach slices in medium saucepan. Bring to simmer over medium-high heat and cook, stirring occasionally, until butter is melted and sugar is dissolved (and frozen peaches are thawed). Remove from heat and let cool for 5 minutes. Transfer peach mixture to blender, add peach preserves and lemon juice, and process until smooth, about 30 seconds. Set aside peach sauce.
Roll dough into 12-inch square, about ⅛ inch thick. Using pizza cutter or chef's knife, trim away and discard outer ½-inch edges of dough to make neat square. Cut dough in half. Working with 1 dough half at a time, cut crosswise into 3 equal rectangles, then cut each rectangle diagonally to create triangles. Repeat with second dough half. (You should have 12 triangles.)
Working with 1 dough triangle at a time, place 1 reserved peach slice on wide end of triangle. Roll dough around peach slice and transfer dumpling, seam side down, to 8-inch square baking pan. Repeat with remaining dough triangles and peach slices, staggering dumplings in 3 rows of 4 (dumplings will touch; this is OK).
Pour peach sauce over dumplings in pan. Combine cinnamon and remaining 1 teaspoon sugar in small bowl. Sprinkle dumplings with cinnamon sugar. Bake until dumplings are golden on top and syrup is bubbling in center of pan, about 45 minutes. Let cool for 10 minutes before serving.