Gather all ingredients.
Stir together milk and vinegar; let stand for a few minutes until thick.
Cream together sugar and shortening in a mixing bowl until smooth.
Beat in egg and vanilla until well-blended.
Sift together flour, baking soda, and salt in a separate bowl; stir into sugar mixture alternating with milk mixture.
Roll dough out on a floured surface to ⅓-inch thickness.
Cut into donuts using a donut cutter. Let stand for about 10 minutes.
Heat oil in a large, deep skillet to 375 degrees F (190 degrees C). Fry donuts in hot oil in batches until golden, turning over once, about 1 to 2 minutes per side.
Drain on paper towels.
Dust with confectioners' sugar while they are still warm and serve.
