Preheat oven to 350°F. Coat a loaf pan (or a mini loaf pan, like I did) with nonstick vegetable oil spray. Dust with flour and tap out the excess.
Whisk 1 1/2 cups all-purpose flour, 2 teaspoons baking powder, and 3/4 teaspoon kosher salt in a medium bowl. Using your fingers, rub 1 cup sugar with 1 tablespoon finely grated grapefruit zest in a large bowl until sugar is moist. Add 3/4 cup whole-milk yogurt, 1/2 cup vegetable oil, 2 large eggs, and 1/2 teaspoon vanilla extract; whisk to blend.
Fold in dry ingredients until just combined. Pour batter into prepared pan. Bake until top of cake is golden brown, 50-55 minutes. Let your delicious cake cool in pan and on a wire rack for 15 minutes.
Whisk together powdered sugar and grapefruit juice until smooth and drizzle over your cake!