Adjust oven rack to middle position and heat oven to 350 degrees. Place phyllo sheets on rimmed baking sheet. Cover with large sheet of plastic wrap. Sprinkle clean dish towel with water until just damp. Place damp towel on top of plastic.
Use pastry brush to paint inside of 9-inch round metal cake pan lightly with a little bit of melted butter.
Remove 1 phyllo sheet from stack (keeping remaining sheets covered) and place on clean counter with long side facing you.
Use pastry brush to paint phyllo with melted butter, then shape into ruffled spiral (see photos, “Step-by-Step: Making Ruffled Milk Pie,” below). Continue to brush each phyllo sheet with butter, scrunch into strip, and add to cake pan until pan is full.
Place cake pan in oven and bake until phyllo is golden brown, 30 to 35 minutes. (This recipe was developed using a light-colored cake pan. If using a dark-colored cake pan, reduce baking time to 20 to 25 minutes.)
While phyllo bakes, in medium bowl, whisk milk, eggs, sugar, vanilla, cinnamon, and salt until well combined.
When phyllo is ready, use oven mitts to remove cake pan from oven and place on cooling rack (ask an adult for help). Pour milk mixture evenly over phyllo in cake pan.
Use oven mitts to return cake pan to oven and bake until filling is set and no longer jiggles when pan is gently shaken (ask an adult for help), 20 to 24 minutes.
Use oven mitts to remove cake pan from oven and place on cooling rack (ask an adult for help). Let pie cool on rack for 30 minutes.
Dust pie with confectioners’ sugar (see photo, “Step-by-Step: Dusting Confectioners’ Sugar on Desserts,” below). Slice pie into wedges and serve warm.