1. Gather all ingredients. 2. Stir together milk and vinegar; let stand for a few minutes until thick. 3. Cream together sugar and shortening in a mixing bowl until smooth. 4. Beat in egg and vanilla until well-blended. 5. Sift together flour, baking soda, and salt in a separate bowl; stir into sugar mixture alternating with milk mixture. 6. Roll dough out on a floured surface to 1/3-inch thickness. 7. Cut into donuts using a donut cutter. Let stand for about 10 minutes. 8. 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. 9. Drain on paper towels. 10. Dust with confectioners' sugar while they are still warm and serve.