Preheat the oven to 350 degrees F. Grease a 9×5-inch loaf pan with butter and flour or a cooking spray with flour in it.
In a small bowl, whisk together the flour, baking powder and salt. In a medium bowl, whisk the eggs. Add the yogurt, brown sugar, oil, grapefruit juice and zest, and almond extract and whisk until combined.
Stir the dry ingredients into the wet, mixing until full combined. Pour the batter into the greased loaf pan and bake for 50 minutes, or until the center is set and a toothpick inserted comes out clean.
Let the cake cool in the pan for 10 minutes, then remove it gently and set it on a cooling rack to cool completely. Once cool, pour the icing over top. Let the icing set, then slice and serve!