Preheat oven to 350˚F. Grease an 8 1/2x 2 1/2-inch loaf pan. Line bottom with parchment, and grease and flour the pan.
Sift together the flour, baking powder and salt in a medium bowl. Whisk together the yogurt, 1 cup of the sugar, eggs, grapefruit zest, and vanilla in a large bowl. Slowly whisk the dry ingredients into the wet ingredients. Use a rubber spatula to fold the vegetable oil into the batter until well incorporated. Pour batter into prepared loaf pan and bake for 50 minutes, or until a toothpick inserted into the center comes out clean.
Simmer the grapefruit juice and last tablespoon of sugar in a small pot over medium heat until the sugar dissolves and the mixture is clear.
Allow the cake to cool in the pan for 10 minutes. Place on a wire rack over a sheet pan. Pour the grapefruit-sugar mixture over the cake and allow it to be absorbed. Let the cake cool, then enjoy.