Preheat the oven to 350°F (180°C). Line a 6-inch or 8-inch round cake pan with parchment paper. Oil sides and bottom of the pan. Set aside.
In a large mixing bowl, whisk vanilla yogurt, oil, and sugar. If your yogurt is unflavored, or your yogurt has a light vanilla flavor, stir in some vanilla extract.
Fold in flour and stir to incorporate until the batter is thick and smooth.
Pour the batter in the prepared pan.
Bake the cake at 350°F (180°C) for 45-50 minutes for a 6-inch pan or 35-40 minutes for an 8-inch pan. Check if the cake is ready by inserting a toothpick in the center of the cake. If it comes out clean, it's ready to remove from the oven. If not, bake longer, in 10-minute increments, until the crumb is set.
Cool down on a cooling rack before at room temperature for 1 hour before serving.
