Preheat oven to 350°F (180°C). Spray an 8-inch round cake pan with baking spray with flour; line bottom of pan with parchment paper.
In a large mixing bowl, whisk flour, sugar, baking powder, and salt together in a bowl until well combined.
Add in orange zest and rosemary and mix well.
Add olive oil, milk, and eggs, and extracts, mixing gently between each addition. Batter will be very liquidy.
Scrape batter into prepared pan and bake until a wooden pick inserted in center comes out clean, approximately 35 minutes. .
Let cool in pan for 10 minutes. Remove from pan, brush with additional olive oil, and let cool completely on a wire rack.
Store at room temperature wrapped loosely in foil or plastic wrap. Dust with powdered sugar just before serving, and garnish with a rosemary sprig.
Olive Oil: I used California Olive Ranch Rich & Robust olive oil because I wanted a more full olive oil flavor. You can use whatever olive oil you like, as long as it has a flavor you enjoy!Storage and Freezing: This cake will keep, covered, at room temperature for up to 3 days, or you can freeze it, well wrapped, for up to 2 months.