Preheat the oven to 350°F. Grease a 9-inch Bundt pan thoroughly with butter.
In a large mixing bowl, beat the caster sugar and eggs with an electric mixer, adding the eggs one at a time. Add the softened butter and continue mixing until light and creamy, about 3 minutes.
In a separate bowl, whisk together the all-purpose flour and baking powder.
Soak the pistachios and hazelnuts in water for 1 minute, then drain well. Toss the nuts with the flour mixture to coat evenly, reserving about 2 tablespoons of pistachios for garnish.
Gradually fold the flour mixture into the egg and butter mixture, mixing gently until fully incorporated.
Pour the batter into the prepared Bundt pan and smooth the top evenly.
Bake for about 40 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then carefully transfer it to a wire rack to cool completely, about 10 minutes more.
To prepare the glaze, whisk the remaining pistachio pudding mix with 1½ cups whole milk in a small bowl until smooth and slightly thickened.
Spread the glaze over the cooled Bundt cake and garnish with the reserved pistachios before serving.