Combine flour, egg yolks, sour cream, sugar, butter, rum, and salt in a large bowl; mix to form a dough.
Knead dough lightly and roll out on a floured surface. Cut into strips 4 inches long and 3/4 inches wide. Cut a slit in the middle of each strip. Twist and pull one end through the slit.
Heat oil in a deep-fryer or large saucepan. Test the temperature by dropping in a pastry twist; the oil is ready when it browns and float to the surface.
Fry pastry twists in batches until golden brown, about 1 minute per side. Drain on a plate lined with paper towels. Dust with confectioners' sugar.
