Preheat oven to 325 degrees F. Grease a 8½- by 4½-inch loaf pan with butter or cooking spray.
In a medium bowl, whisk together flour, baking powder and salt. In the bowl of a stand mixer (or a large bowl, using a hand mixer) set on a medium speed, beat together butter, sugar and grapefruit zest until light and fluffy, 4 to 5 minutes. Add eggs, one at a time, beating to combine after each addition.
Turn the mixer to low and gradually add the flour mixture, milk and grapefruit juice. Beat until just combined. Take care not to overbeat or the bread will be tough. Pour the batter into prepared pan and level with a spatula.
Bake until a toothpick inserted in the center comes out with only a few crumbs attached, 50 to 60 minutes. Let the bread sit in the pan for 10 minutes. Run a knife around the outside and turn the pan upside down to release the bread. Let cool on a wire rack for 1 hour, then glaze.
The Glaze:
In a medium bowl, whisk together powdered sugar, grapefruit juice and zest, and salt until combined. Drizzle over cooled quick bread.
Notes
Adapted from The America's Test Kitchen Family Baking Book