Preheat the fryer to 350 degrees.
In a small mixing bowl, combine the yeast, 1 teaspoon sugar, and 1/4 cup of the warm water. Stir to dissolve and set aside. In an electric mixer, beat the eggs and remaining 3/4 sugar until thick and pale yellow in color. Change the mixer attachment to a dough hook. With the machine running slowly add the yeast mixture, melted butter, milk, half and half and salt. Add the flour, 1 cup at a time. Mix until the mixture forms a soft ball, leaves the sides of the bowl, and climbs up the dough hook. Remove the dough and turn into a lightly oiled bowl. Cover the bowl with plastic wrap and set the bowl in a warm, draft free space. Let the dough rise until double in size, about 1 1/2 hours. Turn the dough out onto a floured surface and dust the surface of the dough with flour. With a rolling pin, roll out the dough, about 1/4 inch thick, in the shape of a rectangle. Using a 3 inch round cutter, cut the dough into circles. Place the rounds on a baking sheet. Cover the dough with a greased piece of plastic wrap (this will prevent the dough from sticking to the wrap) and let the dough rise until double in size, about 30 minutes. Gently fry a couple of the circles at a time, until golden brown, about 3 to 4 minutes, flipping occasionally for overall browning. Remove the doughnuts from the oil and drain on a paper towel-lined plate. Fit each pastry bag with small round tips. Fill each bag with a different filling. Pipe the donuts, alternately with the different fillings. Sprinkle some of the filled donuts with powdered sugar. Glaze the remaining donuts with the two different glazes. Place on a serving platter and serve.
Yield: 2 dozen doughnuts