Heat the oven to 180C (350F) and lightly oil a 6 hole donut pan with a flavorless oil. Mix all the dry ingredients together in a large bowl, and mix all the wet ingredients, (excluding the carrot), in a large jug.
Pour the wet ingredients into the dry and mix with a spatula to combine. Then stir through the carrot to distribute.
Fill the donut pans 2/3 full by using a teaspoon to spoon the mixture into the pan and place in the oven for 8-10 minutes. Keep an eye on them to make sure they don't become too brown
Leave to cool in the pan for 5 minutes before inverting onto a wire wrack to cool completely. Fill the pan with the remaining mixture and repeat the cooking and cooling process.
Cream cheese and pistachio frosting
Mix all the ingredients together, bar the pistachios, in a large bowl. Taste and add more icing sugar as desired.
Ice the donuts by gently dunking each one into the frosting, giving it a twirl, and then removing. Top up with extra frosting applied with a spoon or small knife.
Sprinkle with the pistachios and eat! Keep in the fridge, in a container, for up to 3 days.