Preheat oven to 180 C. Grease and flour a large bundt cake tin and set aside.
Sift flour, baking powder, bicarbonate of soda and salt into a large bowl.
Place sugar, olive oil, buttermilk, lemon juice and zest, vanilla and eggs into another large bowl and whisk until thoroughly combined.
With a wooden spoon, fold the dry mixture into the liquid until well combined.
Spoon into the prepared bundt tin and bake for 40-45 minutes, until well risen and golden. A skewer, inserted into the centre of the cake, will come out clean when it is ready.
Cool in the tin for 15 minutes before transferring to a wire rack to cool completely.
To prepare the lemon drizzle, sift the icing sugar into a bowl and stir in the lemon juice. You may need a little bit more lemon juice to reach the desired consistency.
Drizzle the icing over the bundt cake, sprinkle with the dried rosemary and leave for the icing to set.
Store in an airtight container.
Notes
If you don't have rosemary infused olive oil use the best extra virgin olive oil you can buy and add two tablespoons of fresh, chopped rosemary.