Spray a 9 x 5 loaf pan with cooking spray and set aside.
Preheat oven to 350 degrees.
Wash the grapefruit thoroughly and zest both into a large bowl. Add the cup of sugar and crumble between your fingers so the sugar and zest are well combined. Juice one of the grapefruit into a liquid measuring cup. ADD ENOUGH GREEK YOGURT TO MAKE 2/3 CUP. My one grapefruit gave me a little less than half a cup of juice.
Whisk the yogurt and juice together and add to the sugar and zest. Add the eggs, oil and vanilla. Whisk well until frothy.
In a separate bowl, whisk together the flour, baking powder and soda, salt and cardamom. Add the dry ingredients to the wet and stir together with a spatula until no streaks of flour remain.
Pour the batter into the loaf pan.
Bake on the center oven rack for 50 - 55 minutes, until center is springy and toothpick comes out clean. Remove cake from pan and allow to cool on a cooling rack.
While cake is baking, juice the other grapefruit. Measure out 3 tablespoons of juice and drink the rest.
Add 1/2 cup of powdered sugar to the juice to start and whisk until smooth. If you'd like the glaze a bit thicker, add another 1/4 cup of powdered sugar.
I drizzled two rounds of glaze on my cake. Once right after it came out of the oven. Once after the cake had cooled.