Start by preheating your oven to 350°F (175°C). Grease a 9x13-inch baking dish to prevent sticking. Preparing the pan in advance ensures the cake releases easily after baking.
In a large bowl, combine the vegetable oil, granulated sugar, brown sugar, honey, and vanilla extract. Mix until the texture becomes smooth and slightly creamy. Add the eggs one at a time and continue mixing until fully incorporated.
In a separate bowl, whisk together the flour, baking soda, salt, cinnamon, and cardamom. This step distributes the spices evenly throughout the cake. Gradually add this dry mixture to the wet ingredients.
Fold the grated carrots and chopped pistachios gently into the batter. Stir until everything is evenly combined but avoid overmixing. This keeps the cake light and tender.
Pour the batter into the prepared baking dish and spread it evenly. Bake for 40–45 minutes or until a toothpick inserted into the center comes out clean. Let the cake cool completely before frosting.
In a mixing bowl, beat the cream cheese, butter, and milk until smooth and fluffy. Add the pistachio pudding mix, pistachio paste (if using), and salt. Slowly mix in powdered sugar until the frosting reaches your desired consistency.
Spread the pistachio frosting evenly over the cooled cake. Sprinkle chopped pistachios on top for extra flavor and texture. Slice and serve your delicious pistachio carrot cake.