Preheat the oven to 450℉.
In a medium bowl, using a pastry cutter, fork, or your hands, cut the flour and shortening together until it resembles a small crumble. Add milk and stir until it's a cohesive ball.
Turn the dough onto a floured surface. Roll into a 12"x20" rectangle. Spread 8 tablespoons of the butter onto the dough in an even layer. If you'd like, sprinkle with nutmeg. Roll the dough up from the short end and cut into 3 individual log rolls. Cut those 3 rolls in half.
Heat the remaining butter in a 13"x9" baking dish in the oven that's preheating to 450℉ until melted. Carefully remove the pan from the oven and place the rolls evenly on the bottom of the pan. (See pictures for how to roll, cut and place in the dish).
For the glaze, in a medium saucepan over medium heat, stir together water, sugar, and vanilla. Heat just until the sugar dissolves and comes to a boil. Carefully pour the syrup on top of the rolls.
Bake 15 minutes, then reduce the heat to 350℉ and bake an additional 20 minutes, or until golden brown on top. Slice and serve with a spoon of the glaze on top. Optional, add a scoop of vanilla ice cream or whipped cream.