In a bowl, mix flour, cocoa, baking powder, and salt. In a small bowl, whisk eggs, sugar, buttermilk, and melted butter to blend. Stir into dry ingredients until well blended. Chill until cold, at least 1 hour or up to 3 hours.
Scrape dough onto a generously floured surface. With floured hands, pat dough out to about 1/2 inch thick. With a 3-inch doughnut cutter, cut out doughnuts. Pat together scraps of dough and cut again. (Alternately, shape dough into ropes about 5 inches long and 1/2 inch thick; join rope ends to form doughnuts.) Place doughnuts on a well-floured baking sheet.
Meanwhile, fill an electric deep-fryer to the fill line or pour about 4 inches of oil into a 5- to 6-quart pan; heat to 375°F Place one doughnut at a time onto a wide spatula and gently slide into oil, frying up to three at a time. Cook, turning once, until puffy and cooked through, 3 to 4 minutes total (to check timing, cut first one to test). With a slotted spoon, transfer doughnuts to paper towels to drain. Repeat to fry remaining doughnuts.
When cool enough to handle, dip the top half of each doughnut in warm mocha glaze and place on a plate. Let stand until glaze is set, about 5 minutes.
Mocha Glaze - In a heatproof bowl, combine 6 ounces chopped semisweet chocolate, 1/2 cup whipping cream, 1 tablespoon butter, 2 teaspoons corn syrup, and 1 teaspoon instant espresso powder. Bring a few inches of water to a boil in a pan; remove from heat. Place bowl over water and let stand, stirring occasionally, until smooth, about 10 minutes.