Preheat oven to 400 F. Butter a 9-inch baking pan.
In a large mixing bowl, sift together flour, sugar, baking powder, baking soda, and salt. Using a pastry blender, cut in the cold shortening and butter until the mixture resembles coarse crumbs. In a small bowl, whisk together the egg, milk and vanilla. Add to the flour mixture and stir into a soft dough ball. Be careful not to over work the dough; handle just enough to bring it together.
Turn out onto a floured surface and roll into a rectangle 12-inches x 10-inches.
In a small bowl combine the filling sugars, cinnamon and nutmeg. Using a pastry brush, brush the surface of the dough with 2 tablespoons of melted butter. Evenly spread the cinnamon sugar filling across the face of the dough.
Starting at one of the long edges, roll the dough tightly into a roll. Using a sharp knife dipped in flour, cut the dough into 8, 3/4-inch pieces. Fill the prepared baking pan with the rounds, placing them close together. Brush the tops with remaining butter. Bake in preheated oven for 13 to 15 minutes, or until golden brown.