Preheat the oven to 350F. Spray a 9-inch round cake pan with cooking spray. Dust lightly with flour too. Set pan aside.
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a small bowl, add the grapefruit zest to the sugar. Rub together with your fingers until fragrant. In a large bowl, mix together the yogurt, sugar, and zest with large spoon or spatula. Whisk in the eggs-you can do all three at once. Mix until smooth and then add in the vanilla and stir again.
Add the flour mixture to the wet ingredients. Mix just until flour is incorporated.
Add the oil and mix well. It might take a minute to get the oil mixed in, but it will.
Pour the batter into your prepared cake pan. Bake for 25-30 minutes, until your cake tester comes out clean and the cake springs back when lightly touched in the center.
Cool on a cooling rack for about 15 minutes and then remove from the pan. While the cake is cooling make the syrup and glaze.
For the syrup, in a small sauce pan add the grapefruit juice and sugar. Whisk over medium heat until the sugar dissolves.
For the glaze, in a medium bowl, whisk together the powdered sugar and grapefruit juice. If it is too thick, add more juice, if it is too runny, add more sugar.
Poke little holes into the cake with a toothpick. Spoon the grapefruit syrup over the cake and let it soak in. Let the cake cool to room temperature and then add the glaze. Drizzle over the top of the cake.