In a large deep pot or fryer heat the oil to 350 degrees F.
In a small mixing bowl, whisk
the yeast, 1 teaspoon sugar, and 1/4 cup of the warm water. Set the mixture aside. In an electric mixer
, and the eggs
until the eggs are 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
, and half and half. Add the 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. Cover the dough with a greased piece of plastic wrap (this will prevent the dough from sticking to the wrap) let the dough rise until double in size, about 1 hour. Using a sharp French knife, cut the dough into 1 inch squares. Fry a couple of the squares at a time, until golden brown, about 3 to 4 minutes, stirring constantly for overall browning. Remove the doughnuts from the oil and drain
on a paper-lined plate. Roll the doughnuts
and serve warm.