2 tablespoons dry (instant or bread machine) yeast
1/2 cup warm water
1/3 cup granulated sugar
1 cup warm milk or water
2 teaspoons pure vanilla extract
2 large eggs, at room temperature
1/3 cup vegetable oil
1 1/2 teaspoons salt
4 1/4 - 5 cups all-purpose flour
Vegetable oil for frying (about 6 cups)
6 ounces semisweet chocolate, melted
1. In a large mixing bowl, stir together yeast and warm water and let stand one minute to allow yeast to dissolve.
2. Stir in sugar, milk (or water), vanilla, eggs, oil, salt, and most of flour together to make a soft dough. Knead 5 to 8 minutes, by hand or with an electric mixer fitted with a dough hook, adding flour as needed to form a firmer dough, until dough is smooth and elastic.
3. If using, remove dough hook and gather dough into a ball. Place in a mixing bowl and then place entire bowl in a plastic bag and lightly seal.
4. Let dough rise until almost doubled in size, about 30-45 minutes.
5. Turn out onto a lightly floured surface and gently deflate. Divide dough into three portions and roll each out to a thickness of about 1/2". Using a 3"doughnut cutter, cut out ring doughnuts. Repeat with each section of dough. Bring scraps together and cut out remaining doughnuts.
6. Place doughnuts on a parchment lined baking sheet. Cover lightly with plastic wrap and let rise until doubled, about 30-45 minutes.
7. When ready to fry doughnuts, fill a wok or heavy Dutch oven two-thirds full with vegetable oil, and heat to 385°F.
8. Carefully transfer doughnuts to hot oil and fry until undersides are deep brown. Turn over once and fry other side for about 90 seconds. Lift doughnuts out using a slotted spoon and drain well on paper towels.
9. Meanwhile, melt white chocolate in a double boiler, over very warm (but not boiling) water. Remove from stove and stir.
10. To finish doughnuts, toss some in granulated sugar and with a fork, drizzle remaining with melted chocolate.