In a large bowl, whisk together the flour, sugar, cocoa powder, baking powder, baking soda, salt, and cinnamon.
In another bowl, beat the eggs and then mix in the buttermilk, melted butter, and vanilla extract.
Pour the wet ingredients into the dry ingredients and stir until just combined. Do not overmix.
Chill the dough in the refrigerator for about 30 minutes to make it easier to handle.
On a floured surface, roll out the dough to about 1/2 inch thick.
Use a donut cutter or two round cutters (one larger and one smaller) to cut out the donuts.
Gather the scraps, re-roll, and cut out additional donuts.
In a deep skillet or fryer, heat about 2 inches of vegetable oil to 350°F.
Carefully place the donuts in the hot oil, a few at a time, and fry for about 1-2 minutes on each side until golden brown.
Remove with a slotted spoon and drain on paper towels.
For the glaze, whisk together the powdered sugar, cocoa powder, milk, and vanilla extract until smooth.
Dip the tops of the cooled donuts into the glaze and let them set on a wire rack.