Put the cinnamon stick, orange peel and water in a medium heavy saucepan and bring to a boil over high heat. Stir in the rice and coconut and cover, reduce heat to low, and cook until rice is tender, about 20 minutes. Uncover, remove and discard cinnamon stick and orange peel.
Add milk, 1/2 cup of the sugar, and salt and mix well. Increase heat to medium. Bring to a simmer and cook, stirring frequently, until very thick, about 15 minutes.
Remove from heat and set aside to cool completely.
Measure about 1/2 cup of the pudding into center of each tortilla, then fold the tortilla in half, pressing gently to close edges. The sticky rice filling acts as glue to keep the empanadas closed.
In a large, heavy bottomed pan, heat vegetable oil (about 1/8-inch high) to 350 degrees (oil should be hot but not smoking). Working in small batches, fry the empanadas, turning after the first side has browned, about 3 minutes per side.
Combine remaining 1/4 cup sugar with ground cinnamon and set aside.
Remove finished emapanadas to paper towels for draining, then sprinkle with cinnamon sugar while still warm.
