In a small bowl whisk the icing sugar with the warm water until smooth and thick. Slowly drizzle in the olive oil and whisk till completely smooth. Add more water or whisked icing sugar if you want it thinner or thicker. I would rather it be on the thicker side for more control.
The pumpkin purée can be replaced with roasted puréed squash, see my Brown Butter Honeynut Squash Bundt Cake for instructions.
The base for this cake is inspired by one found in Aran Goyoaga's book, Cannelle et Vanille