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Combine first 3 ingredients in a the bowl of a stand mixer. Let stand 5 minutes or until bubbly. If it doesn't get bubbly, toss the mixture and start over. Add sour cream and egg to yeast mixture; stir until smooth. Combine flour and salt. Add flour mixture to yeast; beat until a sticky mixture forms. Switch to a dough hook and knead until smooth and elastic, about 3 minutes.
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Place dough in a clean bowl coated with cooking spray. Cover dough with plastic wrap. Let rise in a warm place, 1 hour or until almost doubled in size.
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Punch dough down. Divide dough into 24 equal portions; roll each portion into a ball. Cover dough with plastic wrap coated with cooking spray; let stand 30 minutes.
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Clip a candy/fry thermometer onto the side of a Dutch oven; add oil to pan. Heat oil to 375F.
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While you wait for the oil to come to temperature, whisk powdered sugar, syrup, and water until no lumps remain.
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Place 8 dough balls in hot oil; fry 2 minutes or until golden and done, turning as necessary. Make sure the oil temperature remains at 375F. Remove doughnut holes from pan; drain. Dip doughnut holes into syrup mixture; remove with a slotted spoon. Drain on a cooling rack over a baking sheet. Repeat procedure 3 times with remaining dough balls and syrup mixture.