Heat your oven to 350°F. Grease a 8 ½ by 4 ¼ -inch loaf pan. Line the bottom and two long sides of the pan with parchment paper.

In a medium bowl, whisk together the flour, baking powder, and salt. In a larger bowl, combine 1 cup of the granulated sugar and the zest and rub them together with your fingertips to extract as much grapefruit flavor as possible. Add yogurt, eggs, and vanilla, if using, to the zest-sugar, whisking to combine. Whisk the flour mixture into the yogurt mixture, then whisk in the oil.

Pour the batter into the prepared pan and smooth it out. Bake for about 50 minutes, or until a cake tester inserted into the center of the loaf comes out clean.

Make the syrup: While the cake bakes, combine ⅓ cup grapefruit juice with 1 tablespoon granulated sugar in a small saucepan, stirring it over low heat until the sugar dissolves.

When the cake comes out of the oven, transfer it to a cooling rack, then pour or brush the grapefruit-sugar mixture over the whole cake. If it seems to resist absorbing, poking holes in the cake with a toothpick can help it better soak in. Let the cake cool completely on the rack.

Make the glaze: Combine the powdered sugar and 2 tablespoons grapefruit juice in a bowl, then drizzle it over the cake.

This cake keeps fantastically for three days at room temperature and close to one week in the fridge.