Preheat the oven to 350 F (177 C). Lightly grease and line the botton of a 9" (23 cm) spring form pan with parchment paper. Set aside.
In a medium sized mixing bowl, whisk the flour, baking powder, baking soda and salt together until well combined.
Pour the sugar into the bowl of a stand mixer fitted with whisk attachment. Add the rosemary and zest the grapefruit straight into the sugar. On low speed, grind the zest and rosemary into the sugar for about 30 seconds. Pour in the extracts. Whisk the extracts into the sugar mixture for another 30 seconds.
Add the eggs to the sugar and whisk on high speed for 4-5 minutes. The mixture should be thick and light yellow in color. Scrape the sides and bottom of the bowl.
With the mixer on medium speed, stream in the olive oil. Once all the olive oil is added, increase the speed to high for 1 minute. Scrape the sides and bottom of the bowl. With the mixer on low speed, stream in the milk.
Stir in the dry ingredients into the wet until just combined. Pour the cake batter into the prepared pan.
Bake the olive oil cake at 350 F (177 C) for 40-45 minutes. The top will be golden brown. The center of the cake should bounce back when lightly pressed and the edges of the cake should pull away slighly from the pan. While the cake bakes, make the grapefruit glaze.
Cool the cake in the cake pan placed on a cooling rack for 20 minutes. Remove the sides of the springfrom pan from the cake. Gently slide the cake off the pan using the parchment on the bottom. Allow the cake to cool completely to room temperature while still on the cooling rack.
grapefruit glaze
Slice open the same grapefruits used in the cake batter. Using an electric juicer or reamer, extract all the juice. Pour the juice into a small sauce pan. Heat the juice over medium high heat for about 10-15 minutes. Once the juice has reduced down to 2-3 tablespoons (30-45 ml) remove the pan from the heat. Pour the reduced juice into a bowl to cool to room temperature.
Pour the powdered sugar into a bowl. Whisk in 1 tablespoon (15 ml) reduced juice into the powdered sugar at a time until you achieve your desired taste and consistency.
Pour the glaze over the room temperature cake. Allow time for the glaze to set. Enjoy!