Grease a 23-cm (9-inch) bundt pan with coconut oil and dust it with all-purpose flour. Set aside.
Preheat oven to 180°C (350°F).
Add oil, sugar, and vanilla to a large bowl and, with a hand-held mixer, beat well for 1 minute.
Add soy yoghurt and beat again until everything is combined.
Sift in flour, baking powder, baking soda, and salt.
Pour milk on top and beat until the batter is smooth.
Bake for 60 to 65 minutes until the cake is done. Stick a toothpick into the centre and if it comes out clean the cake is done.
Let cool for 15 minutes.
Use a small knife (preferably a very flexible plastic knife) to loosen the edges, especially around the tube in the centre.
Turn the pan around and let the cake slide on a cookie rack to cool completely.