Heat butter until melted. Remove from heat. Stir in confectioners' sugar and vanilla extract until smooth. Stir in water, 1 tablespoon at a time, until desired consistency.
Heat butter and chocolate over low heat until chocolate is melted; remove from heat. Stir in confectioners' sugar and vanilla extract until smooth. Stir in water, 1 tablespoon at a time, until of desired consistency.
Dissolve yeast in warm water in a 2 1/2-quart bowl. Add milk, salt, sugar, eggs, shortening and 2 cups flour. Beat on low speed scraping bowl constantly, 30 seconds. Beat on medium speed scraping bowl occasionally, 2 minutes. Stir in remaining flour until smooth.
Cover and let rise in warm place, until double, 50 to 60 minutes. (Dough is ready when indentation remains when touched.)
Turn dough onto floured surface; roll around lightly to coat with flour. Gently roll dough 1/2-inch thick with floured rolling pin. Cut with floured doughnut cutter. Cover and let rise until double, 30 to 40 minutes.
Heat vegetable oil in deep fryer to 350°F. Slide doughnuts into hot oil with wide spatula. Turn doughnuts as they rise to the surface. Fry until golden brown, about 1 minute on each side.
Remove carefully from oil (do not prick surface); drain. Dip the doughnuts into Creamy Glaze. Set on rack; when slightly cooled spread Chocolate Glaze on top.
Doughnuts may be dipped into sprinkles or other toppings after. Chocolate Glaze is applied if desired.