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Make donut dough: Mix together 3 1/4 cups flour, 1 cup warm milk, 2 oz room temperature butter, 3 yolks, 2 tbsp sugar and the proofed yeast mixture in mixer on low speed, with the dough hook attachment until the dough comes together, about 2 minutes.

Stir the vinegar into the milk, and let stand for a few minutes until thick. In a medium bowl, cream together the shortening and sugar until smooth. Beat in the egg and vanilla until well blended. Heat the oil in a large deep skillet to 375 degrees F (190 degrees C). Fry doughnuts in the hot oil until golden, turning over once.

Directions. In a medium bowl, cream together the shortening and sugar until smooth. Beat in the egg and vanilla until well blended. Sift together the flour, baking soda, and salt; stir into the sugar mixture alternating with the vinegar and milk. Roll dough out on a floured surface to 1/3 inch thickness. Cut into doughnuts using a donut cutter.

Make glaze: In a large bowl, whisk together milk, powdered sugar, and vanilla until smooth. Set aside. Line a large baking sheet with paper towels. In a large dutch oven over medium heat, heat 2” oil to 350. Cook doughnuts, in batches, until deeply golden on both sides, about 1 minute per side.