Stir the vinegar into the milk and set aside until milk thickens. In a medium bowl, mix together the shortening and sugar until well incorporated.
Beat in the egg and vanilla until all of the lumps are gone and mixture is smooth.
In a small bowl sift together the cocoa, flour, baking soda, and salt. Alternate stirring in flour and milk into the egg mixture until a soft dough forms.
Dust a work surface with flour and briefly knead the dough. Pat out the dough into a disc and roll out to about 1/3-inch thickness.
Using a donut cutter, a biscuit cutter, or a glass, cut out as many donuts as you can. Re-roll out dough scraps to use up all of the dough. If you don't have a donut cutter, use your fingers to poke a hole in the middle.
Lay out doughnuts on a wax paper lined tray and let stand for 10 minutes. Heat the oil to 375 degrees. While waiting for the oil, make the glaze.
In a bowl , whisk together strawberry puree and confectioners sugar, set aside.
To fry donuts, gently drop 3-4 donuts in the hot oil and cook for 1-2 minutes on each side, flipping once ( the handles of wooden spoons or wooden chopsticks are the best tools here). Remove from the oil and drain on paper towels. Continue with the rest.
To glaze the donuts, dip a slightly cooled donut into the glaze and place back on the wax paper tray .