In a large mixing bowl, combine flour, sugar, baking powder, and salt. Cut butter and shortening into dry ingredients, using a pastry blender or fork until it resembles coarse meal.
In a separate bowl, whisk together heavy cream and egg. Split the vanilla bean in half lengthwise and scrape out the beans. Add the vanilla beans to the half and half and egg mixture, whisk to combine. Add wet ingredients to dry ingredients. Stir just until combined.
Knead dough 5-6 times on a generously floured surface, folding dough in half on top of itself each time. Divide dough into 3 equal portions. Roll or pat each portion into a 5-inch diameter dome, with center slightly higher than the outside edge. Cut each dome into 4 wedges.
Bake on an un-greased or parchment lined baking sheet. Bake for 15-17 minutes or until lightly brown. Remove from pan and allow to cool on a rack. Once cooled, prepare glaze.
GLAZE: Pour the half and half and vanilla extract into a medium bowl. Split the vanilla bean in half lengthwise and scrape out the beans. Stir beans into half and half; allow to sit for awhile. Add confectioners' sugar to the vanilla milk, beat until completely smooth. Add more confectioners' sugar or milk if necessary to get the right consistency and thickness.
One at a time, carefully dunk each cooled scone into the glaze, turning it over if necessary. (I don't glaze the bottom, but you can if you want to) Transfer to parchment paper or the cooling rack. Allow the glaze to set completely, about an hour. Scones will keep several days if glazed.