1. In large bowl, whisk together flour, ½ cup cocoa powder, granulated sugar, baking powder, baking soda, and salt until thoroughly combined.

2. In separate medium bowl, whisk eggs until smooth. Add buttermilk, ¼ cup melted cooled butter, and 2 teaspoons vanilla extract. Whisk until fully combined.

3. Pour wet ingredients into dry ingredients all at once. Stir gently with wooden spoon just until combined—don’t overmix. Dough will be soft and slightly sticky.

4. Cover bowl with plastic wrap and refrigerate for 30 minutes to firm dough for easier cutting.

5. Turn chilled dough onto generously floured surface. Dust top with more flour. Pat or gently roll to ½-inch thickness.

6. Using floured 3-inch round cutter, cut doughnut rounds. Use floured 1-inch cutter to cut out centers. Save doughnut holes. Place on parchment-lined baking sheet dusted with flour.

7. Heat 3-4 inches oil in large heavy pot to exactly 375°F using thermometer clipped to pot side.

8. Carefully slide 2-3 doughnuts into hot oil using slotted spoon. Fry 60-90 seconds on first side until deep golden brown. Flip and fry second side 60-90 seconds.

9. Remove with slotted spoon and place on wire rack over paper towels to drain. Cool 5 minutes before glazing.

10. Make glaze: Whisk powdered sugar and ¼ cup cocoa powder in medium bowl. Add 2 tablespoons melted butter, 1 teaspoon vanilla, pinch salt, and 3 tablespoons milk. Whisk until smooth, adding remaining milk if too thick.

11. Dip top of each slightly cooled doughnut into glaze, letting excess drip off. Return to wire rack and let set 10-15 minutes until glaze firms to glossy finish.