Preheat the oven to 180C/356F. Place an ovenproof dish or cake tin half filled with boiling water in the base of your oven. This will create a steamy environment to keep the cakes moist and prevent them browning too much.
Grease two 20cm cake pans (not spring form) with a small amount of oil and line them with baking paper.
Combine the flour, sugar, baking powder, baking soda and salt in the bowl of your KitchenAid. Use the paddle or whisk attachment on a low speed to combine.
In another medium mixing bowl, whisk together the yoghurt, milk and vinegar or lemon juice. The mixture should become smooth and thicker quite quickly.
Add the yoghurt mixture, eggs and vanilla bean paste to your KitchenAid. Beat the mixture on a low smooth until you have a smooth and fluffy batter, free of any lumps.
Divide the mixture between the two cake tins, then place them into the oven. Bake for 15 minutes, then swap them around in the oven (to account for any heat spots that might cook one cake more quickly) and bake for an additional 15-25 minutes. A baked cake should be well browned and not wobbly if you shake the cake tin. A skewer should come out clean.
Set the cakes aside to cool completely.