Oil a large mixing bowl with the vegetable oil and set aside.

In a small mixing bowl, combine the yeast, 1/2 teaspoon of the sugar, and the water. Stir and set aside until foamy, about 5 minutes.

With electric mixer, beat the eggs and the remaining 6 tablespoons of sugar until thick and pale yellow in color, about 6 minutes. Change the mixer attachment to a dough hook. With the machine on low speed, slowly add the yeast mixture, melted butter, milk, half-and-half, and salt. Add the flour, 1 cup at a time, and mix until the dough forms a soft ball that leaves the sides of the bowl and climbs up the dough hook. Turn out into the oiled bowl, turning to coat on all sides. Cover with a kitchen towel and set aside in a warm, draft-free place until doubled in size, 1 to 1 1/2 hours.

Turn out the dough onto a floured work surface and dust lightly with flour. Roll out into a rectangle about 12 by 17 inches and 1/2-inch thick. Cover with a lightly-oiled piece of plastic wrap. Put the dough in a warm, draft-free place and let rise until doubled in size, about 1 hour.

Heat 6 inches of oil in a deep, heavy pot, or an electric fryer, to 360 degrees F.

With a sharp knife, cut the dough into 2-inch squares. Flour your hands, then pat the squares down a little to lightly flatten them. Fry in batches until golden brown, 3 to 4 minutes, turning them to brown evenly. Drain on paper towels and sprinkle with the sugar. Serve warm.