Preheat oven to 350°F. Melt butter in a 13"x9" baking dish in the oven while it's preheating. Once melted, remove and set aside.
For the filling, in a small bowl, toss together the diced apples and cinnamon until all of the pieces are coated well.
For the dough, in a large bowl, cut shortening into the self-rising flour until it resembles coarse crumbs.
Add milk to the flour mixture gradually, mixing until a soft dough forms.
Turn the dough onto a lightly floured surface and roll into a large rectangle about 1/4-inch thick.
Evenly distribute the apple mixture on top of the dough, leaving about 1/2-inch of the dough all around the exterior uncovered.
Roll up the dough starting from one long side to form a log. Dampen the edges of the dough with water to seal.
With a sharp knife, cut the log into 16 slices and place them in one layer in the prepared baking dish.
For the syrup, in a medium saucepan over medium heat, stir together 2 cups of water and sugar. Heat just until the sugar dissolves and comes to a boil, then turn off the heat. Pour the syrup over the apple rolls.
Bake 55-60 minutes or until the rolls are golden brown and the apples are tender. Allow to cool slightly before serving. Enjoy warm with vanilla ice cream, fresh whipped cream, or a dusting of powdered sugar.