Line the muffin tin with cupcake cases and set it aside. Preheat the oven to 170C/340F whilst making the carrot cake batter.
In a large jug or bowl, tip together the oil, buttermilk, sugars, vanilla and eggs. Whisk to combine, then add in the grated carrots and stir to mix it all together. Set aside.
In a separate large bowl, sift together the flour, baking powder, bicarbonate of soda (baking soda), salt and spices, giving it a quick mix together. Pour in the wet ingredients and mix it all together with a spatula. Finally, tip in the broken walnuts and stir through.
Using an ice cream scoop or two tablespoons, divide the carrot cake mixture between the prepared cupcake cases. Bake in the preheated oven for 20-25 minutes until springy to touch and a wooden skewer inserted comes out clean. Cool for five minutes in the tin, then transfer the cupcakes to a cooling rack and cool completely.