For the grapefruit cake: Preheat oven to 350 degrees F. Coat a 9×5-inch loaf pan with nonstick cooking spray. Place a strip of parchment paper in the bottom of the pan. (This makes for easy removal!)
In a medium bowl, whisk flour, baking powder, and salt together. In the bowl of a stand mixer fitted with the paddle attachment, beat eggs and sugar together on medium speed for about 3 minutes, until thickened. Blend in milk, oil, and vanilla. With mixer on low speed, beat in dry ingredients until just combined; do not overmix.
Pour the batter into the prepared pan. Bake for 1 hour, or until a toothpick inserted in the center comes out with just a few moist crumbs attached.
For the syrup: While cake bakes, prepare the syrup. In a small saucepan set to medium-high, combine grapefruit juice and sugar. Bring to a boil, then reduce to a simmer, stirring to dissolve the sugar completely. Continue to simmer for 1 minute.
Once fully baked, remove cake from the oven. Keep cake in pan and with a skewer, poke deep holes all over the cake. Pour syrup over top of cake. (It may seem like the cake is drowning in syrup at first, but it will all soak in and make the cake very moist.)
Refrigerate cake, still in pan, and let cool. Once completely cool, remove from pan and garnish with grapefruit slices and mint leaves, slice and serve. Or, top with frosting (recipe below), garnish and slice.
For the frosting: Add frosting mix and butter to a large bowl. Blend with an electric mixer on low speed for 1 minute, until well blended. Scrape sides of bowl with a rubber spatula. Add water and mix on low speed, until combined. Scrape bowl. Beat on high speed for 30 seconds.
Frost cake (a small rubber spatula works best for this) and top with grapefruit slices and mint leaves, if desired. Serve immediately, or wrap with plastic wrap and refrigerate until ready to serve.
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