Preheat your oven to 180C / 160C (fan) / 350F. Prepare a 32x21.5cm (12.5x8.5in) rectangular baking tin by greasing and lining with non-stick baking paper. The baking paper should go over the edges so you can use the paper to lift out the cake once it's cooled.
In a large mixing bowl, add the oil, light brown sugar and eggs. Mix together (I use an electric hand whisk for this part) until well combined.
Next, sift in the flour, bicarbonate of soda, xanthan gum, cinnamon and ginger. Gently fold these in to the mixture using a silicone spatula.
Add the orange zest and grated carrot (at this stage you could add chopped walnuts, pecans or raisins if you like - I don't like raisins so sometimes choose to add nuts, but often don't bother!) Fold into the mixture so the carrot and orange zest is evenly dispersed.
Spoon/pour the mixture into your baking tin and place in the oven for about 60 minutes. The cake should be cooked through, use a skewer to check.
Leave the cake to cool in the tin until it firms up a bit. Then, carefully lift it out using the baking paper and then onto a cooling rack to cool completely.
To make the cream cheese frosting, mix the softened butter in a stand mixer or with an electric hand mixer (in a mixing bowl) at a medium speed for 5 minutes or until paler in colour. Add the icing sugar and beat for about 3 minutes.
Add in the cream cheese and vanilla and beat for 2–3 more minutes until well combined and the icing is light and fluffy, without lumps. Place in the fridge to chill briefly until you need it.
Spread the frosting evenly all over your cake. With a carrot cake being a bit more delicate, be careful when spreading so none of the top layer comes off... it doesn't really matter if it does!
Sprinkle the top of your cake with chopped up walnuts or pecans.
Cut your cake into 12-15 squares and enjoy!