Preheat the oven to 350 degrees F (175 degrees C). Lightly grease a 7x11-inch baking pan.
In a large bowl, mix together flour and salt. Cut shortening in thoroughly with a pastry blender until the mixture resembles breadcrumbs. Stir in water and press dough together with your hands. Roll out the pastry into a large rectangle. Spread butter evenly over the pastry, then sprinkle on 1/4 cup sugar and nutmeg. Roll up the dough jelly roll style and pinch to seal. Cut into 12 even slices. Place the rolls in the prepared pan.
In a small saucepan, heat milk, 2/3 cup sugar, and vanilla until the mixture begins to bubble. Pour milk mixture over rolls.
Bake in the preheated oven until brown, about 30 to 40 minutes.