1. In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and granulated sugar.

2. In a separate bowl, whisk the eggs, buttermilk, melted butter, and 2 teaspoons vanilla until smooth.

3. Add the wet ingredients to the dry ingredients and mix just until a soft dough forms.

4. Turn the dough onto a lightly floured surface, roll gently, and cut into round donuts suitable for filling.

5. Heat oil in a deep pan over medium heat until hot enough for frying.

6. Fry the donuts in batches until golden brown on both sides, then transfer to paper towels to drain.

7. Whip the heavy cream until soft peaks form, then fold in the pistachio paste to make the filling.

8. Once the donuts are cool enough to handle, pipe the pistachio cream into the center of each donut.

9. Whisk together the powdered sugar, milk, and remaining 1/2 teaspoon vanilla to make the glaze.

10. Dip the tops of the filled donuts into the glaze and finish with crushed pistachios before serving.