Preheat oven to 350°. Prepare baking pan by coating the bottom and halfway up the sides with butter (about 1 tbsp butter) and then sprinkle 1 tsp of sugar in pan and tap pan on all sides so that sugar coats all the butter.
In a medium bowl, mix flour, shredded coconut, and baking powder.
In a large bowl, use a zest grater to zest both grapefruits. In a separate small or medium bowl, juice the zested grapefruits. Set aside for later.
To the zest, add ¼ cup of the sugar and with your fingers mash the sugar with the zest so that the sugar coats all the zest flakes. Set aside 1 tbsp of zest mixture to use later for the frosting.
To the large bowl with zest, add the remaining ¾ cup of the sugar and room temp butter. Cream together until paler and fluffy.
Add eggs, one by one and making sure that each is incorporated into the batter.
Take ½ cup of the reserved grapefruit juice and add it to the batter. Keep the remaining juice for later use in the frosting.
Once juice and eggs are mixed into the batter, take the flour mixture and in two batches, pour into the butter batter. Try not to over mix.
Pour into buttered and sugared loaf pan and place in oven for 30-35 minutes. Check for doneness by inserting a toothpick or sharp knife into batter to see if it comes out clean (if not, add a few more minutes to the bake time).
Let cool once removed from oven (about 45 mins).
For the frosting: whisk together 1 cup powdered sugar, remaining grapefruit zest and ¼ cup grapefruit juice to produce a white and runny frosting.
Using a spoon or spatula, drizzle the grapefruit frosting onto the cake, making sure the top is completely covered. Or if you prefer a minimal frost top, use as little or as much frosting as you like.
Let frosted cake stand (about 30 mins). Cut and serve. Cake can be wrapped in cling wrap or stored in airtight container for up to 3 days. It can also be cut and stored in the freezer for future use.