Preheat the oven to 350°F (175°C) and grease and flour a 9-inch round cake pan.
Cream together the softened butter and granulated sugar in a mixing bowl until light and fluffy.
Add the eggs one at a time, beating well after each addition, then stir in the vanilla extract and cooled coffee.
Whisk together the flour, baking powder, baking soda, and salt in another bowl.
Gradually combine the dry mixture with the wet ingredients, mixing until just combined, then fold in the chopped pistachios.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 30-40 minutes, or until a toothpick inserted into the center comes out clean.
Cool in the pan for 10 minutes before transferring to a wire rack to cool completely.
Whisk together the powdered sugar, cooled coffee, and vanilla extract in a small bowl until smooth.
Drizzle the glaze over the cooled cake before serving.