Preheat the oven to 350 degrees F (180 C). Generously butter and flour a 9-inch bundt pan; set aside.

In a medium bowl, whisk together the flour, baking powder, and salt; set aside.

In a large bowl or bowl of a stand mixer, combine the sugar and grapefruit zest. Rub the mixture together with your hands for 1-2 minutes, until evenly-combined.

Add the eggs, and using the whisk attachment of a hand or stand mixer, beat on medium speed for 2-3 minutes, until the mixture is thick and creamy. 

Beat in the milk, followed by the oil and the vanilla. Add the dry ingredients, and beat on low speed just until combined. 

Scrape the batter into the prepared pan. Bake for 45-60 minutes, just until a toothpick inserted into the cake comes out clean.

Let cake cool for 20-30 minutes on a wire rack, then invert the pan onto a cake plate or platter and allow to cool completely.

To make the grapefruit syrup, combine grapefruit juice and sugar in a small saucepan. Bring to a simmer, stirring to dissolve the sugar, then continue to simmer for 2-3 minutes. When the cake has been cooled and inverted, prick the top all over with a toothpick, then generously spoon over the syrup.

To make the glaze, whisk together powdered sugar and grapefruit juice. Begin with just 1 tablespoon of juice, then add more a small amount at a time until the glaze reaches your desired consistency. Pour glaze over cake, sprinkle with additional zest if desired, and serve.