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1
In a small mixing bowl, combine the yeast, 1 teaspoon of the sugar, and the water.
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2
Stir to dissolve the sugar and set aside.
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3
If the yeast doesn't foam after a few minutes, you need to buy new yeast and start again.
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4
In an electric mixer, beat the eggs and the remaining 3/4 cup sugar until thick and pale yellow in color, about 6 minutes.
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5
Change the mixer attachment to a dough hook.
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6
With the machine on low speed, slowly add the yeast mixture, melted butter, milk, half-and-half, and salt.
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7
Add the flour, one cup at a time, and mix until a soft ball forms that leaves the sides of the bowl and climbs up the dough hook.
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8
Remove the dough and turn into a lightly-oiled bowl, turning to oil all sides.
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9
Cover the bowl with plastic wrap and set the bowl in a warm, draft-free place until it doubles in size, about 1 1/2 hours.
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10
Turn the dough out onto a floured work surface and dust it with flour.
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11
Roll out the dough into a rectangle about 12x17 inches and 1/2 inch thick.
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12
Cover the dough with a lightly-oiled piece of plastic wrap.
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13
Put the dough in a warm, draft-free place and let rise until doubled in size, about 1 hour.
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14
Heat 6 inches of oil in a deep, heavy pot, or an electric fryer, to 360 degrees F.
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15
With a sharp knife, cut the dough into 2-inch squares.
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16
Flour your hands, then pat the squares down a little to lightly flatten them.
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17
Fry the squares, 2 to 3 at a time, until golden brown, 3 to 4 minutes, turning them to brown evenly.
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18
Drain on paper towels.
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19
Sprinkle the doughnuts with sugar and serve warm.
