In the bowl of a stand mixer fitted with a paddle attachment or a large bowl, combine the flour, sugar, cocoa powder, baking powder, and salt.
Make a well in the center and add the buttermilk, butter, eggs, vinegar, vanilla extract, and red food coloring.
Mix just until the ingredients are evenly combined.
Cover the bowl and refrigerate for 1 hour to allow the dough to become firm and easier to handle.
Place a sheet of parchment on a work surface and cover with a generous dusting of flour.
Remove the dough from the refrigerator, dust the top with flour, and roll into a thin sheet about 1/3 inch (8 millimeters) thick, adding more flour just as needed to prevent sticking.
Use a doughnut cutter or a 3 1/2 inch (9 centimeter) round cutter with a 1 1/2 inch (4 centimeter) smaller round cutter in the center to make individual doughnuts.
Pour 2 inches (5 centimeters) vegetable oil into a heavy saucepan and place over medium low heat to 340˚F (170˚C), no higher.
Once heated, add 2-3 doughnuts (I sometimes test the oil first with a smaller doughnut hole).
Fry for about 1 1/2-2 minutes (a little less for the donut holes) per side until puffed and lightly golden.
Use a spider strainer to remove the cooked donuts to a paper towel lined plate or baking sheet.
Repeat with remaining dough, bringing together the scraps and recutting as many as possible.