Combine 4 cups flour and all remaining ingredients except oil and additional sugar in bowl. Beat at low speed, scraping bowl often, until well mixed. Stir in enough remaining flour to make dough easy to handle.
Turn out dough onto lightly floured surface; knead 2 minutes or until smooth. (Do not over knead.)
Divide dough in half; roll each half to 3/8-inch thickness. Cut out doughnuts with lightly floured 2 1/2-inch doughnut cutter.
Heat 3 inches oil in deep fat fryer or Dutch oven to 375°F.
Place 2 to 3 doughnuts in hot oil. Fry 2-4 minutes, turning once, or until golden brown on both sides. Remove from oil; drain on paper towels. Repeat with remaining doughnuts. Sprinkle with sugar, if desired.
*Substitute 2 tablespoons vinegar or lemon juice and enough milk to equal 2 cups. Let stand 5 minutes.
It is important to roll the dough to correct thickness. If rolled thicker, the doughnut though browned may not be cooked through. If rolled thinner, the doughnuts will be dry and over browned.
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