Grease a 6 inch (15cm) round cake pan with a little oil or butter and line the base with baking paper.
In a small bowl, whisk together the plain flour, baking powder, baking soda and salt. Set aside.
In a separate bowl, cream the butter, caster sugar and oil together with an electric hand mixer, or a stand mixer fitted with the paddle attachment, until the mixture is pale and fluffy. This takes around 3 minutes.
Add the eggs, vanilla and yoghurt and beat until smooth and combined. If the mixture looks slightly split at this stage, it will come back together once the flour is added.
Add the dry ingredients to the wet mixture and mix on low speed, or fold them through with a spatula, until just combined with no dry flour visible. Don't overmix.
Spoon the batter into the prepared pan and smooth the top. Place the pan into the air fryer basket, leaving a little room around it so the air can circulate.
Bake at 160°C (320°F) for 25 minutes. Insert a skewer into the centre of the cake. If it comes out clean, the cake is done. If it isn't clean, lower the temperature to 150°C (300°F), bake for another 5 minutes and check again, repeating until the skewer comes out clean.
Let the cake cool in the pan for 5 minutes, then turn it out onto a wire rack to cool completely.
Dust with icing sugar, or frost and decorate as you like.