Special equipment: large deep fryer
In a small bowl proof yeast in lukewarm water and sugar for 15 minutes, or until it is foamy. In a large bowl with an electric mixer beat 1 large egg with 1/3 cup sugar and 1/2 teaspoon salt until the mixture is thick and light, beat in the yeast mixture, lukewarm milk, and melted and cooled butter, and gradually add all-purpose flour, or enough to form a soft dough. Knead the dough on a floured surface for 5 minutes, or until it is smooth and elastic, and form it into a ball. Put the dough in a buttered bowl, and let it rise, covered with plastic wrap, in a warm place for 1 hour and 30 minutes, or until it is double in bulk. Punch down the dough and on a floured surface roll it out 1/3 inch thick. With a 21/2 --inch cutter dipped in flour, cut out rounds. Gather the scraps into a ball, re-roll the dough, and cut out doughnuts in the same manner. Transfer the doughnuts and holes with a spatula to a baking sheet sprinkled lightly with flour and let rise, uncovered, in a warm place for 30 minutes to 1 hour, or until they are double in height.
In a large deep fryer heat 3 inches vegetable shortening or vegetable oil to 375 degrees and in it fry the doughnuts, 4 at a time, for 1 1/2 minutes on each side, or until they are golden brown and puffed, transferring them with a skimmer as they are fried to paper towels to drain. Fill a pastry bag with the creme filling and fill the warm doughnuts. Spread chocolate glaze on top of the doughnuts, and transfer them with tongs to a rack set over wax paper to dry.
Combine the milk and half the sugar in a non-reactive saucepan. Whisk once and place over medium heat to come to a boil. Meanwhile, whisk the yolks and salt in a bowl and whisk in the remaining sugar. Sift the flour over the yolks and mix in. When the milk boils, whisk a third of the boiled milk into the egg mixture, whisking constantly. Pour the egg mixture back into the pot. Continue whisking until the cream thickens and comes to a boil. Remove from the heat and whisk in the vanilla. Before chilling the pastry cream, recheck the recipe in which it is used for other ingredients to be added before the pastry cream is chilled. Pour the cream into a heat-proof glass or stainless-steel bowl or pan. Press plastic wrap directly against the surface of the cream. Chill immediately. Use the pastry cream by the end of the following day.
In the top of a double boiler set over simmering water melt semi-sweet chocolate with unsalted butter. Stir in milk and vanilla and combine the mixture well. Add gradually sifted sugar, beating and beat the glaze until it is smooth.;