Line and lightly grease a 21.5cm x 11.4cm x 6.9cm loaf tin and preheat the oven to 180°C/350°F (conventional/standard) / 160°C/320°F (fan).
In a large mixing bowl, beat the butter and sugar together with a hand mixer until it resembles fluffy sand. (You can also do this step in a stand mixer)
Add half the yoghurt and keep beating until combined. Add the second half and mix that in as well.
A tablespoon at a time, beat in the olive oil and finally all the vanilla. Set the mixture aside.
In a separate bowl, whisk together the flour, baking powder and soda and the salt. Add half the dry ingredients to the wet and mix through with a large spoon before adding the second half. Mix until combined but no more.
The batter is super thick, don't worry it's supposed to be.
Spoon the batter into your prepared loaf tin and using a spoon or baking palette knife, smooth it out nice and level.
Pop the loaf in the oven and bake for 50-60 minutes or until a skewer comes away from the centre clean.
Remove the loaf from the oven and allow it to sit for at least 10 minutes before turning it out onto a cooling rack. The longer you leave it, the easier the cake is to handle. The crumb settles and it's just easier to cut.
Slice and serve at room temperature.