Set oven to 180℃ or 350℉ (or 160℃ fan)
Spray a 20cm (8 inch) square pan with oil and line with baking paper (parchment paper)
In the bowl of your stand mixer (or large mixing bowl, if you’re using a hand mixer) place the sugar and zest. Rub the zest into the sugar for about 30 seconds, until it starts to release the oils and become a little clumpy
Add the butter, then use the paddle attachment to beat at medium speed for 2 minutes. Stop the mixer and scrape the bowl, then mix again on medium-high speed for another minute, until mixture is fluffy
Add the remaining wet ingredients and mix on low, gradually increasing to medium speed for about 4 minutes (mixture will look a little funky at this stage, but don’t worry!). Scrape the bowl as necessary.
Combine the plain flour (all purpose flour), baking powder and bicarb soda in a small bowl, then add a spoonful at a time of the flour mixture to the mixing bowl.
Once all of the flour has incorporated into the mixture, scoop it out and spread it into your prepared cake pan.
Bake for 40-45 minutes, until lightly golden. Use a cake tester or skewer to check that the cake is done
Remove cake from the oven and cool in the pan for 5 minutes, before lifting it out by the baking paper to rest on a cooling rack.
Either dust with icing sugar and serve, or let cool completely before drizzling over the Vanilla Bean Icing