1In a small saucepan, bring water, sugar and rosemary for syrup to a simmer. Remove from heat and allow to cool. Set aside Rosemary sprig for cake. Remove the leaves from the stem and finely chop. Transfer the simple syrup once cool enough to a jar and chill in the refrigerator.
Preheat oven to 350 degrees.
Sift together flour, baking powder, and salt. Set aside.
In the bowl of a stand mixer, beat together sugar, butter and oil until smooth. Add eggs, one at a time. Add vanilla, lemon zest, and rosemary. Mix until well combined. Alternately add milk and dry ingredients, beginning and ending with the dry ingredients.
Pour into an 8½ inch cake pan. Bake for about 30-35 minutes or until cake tester comes out clean. Transfer cake to a wire rack and allow to cool completely in the cake pan.
With a sharp knife, poke the cake several times and drizzle with about ½ cup of Rosemary simple syrup. Cover the cake and place in the refrigerator for a couple of hours or overnight.
Whisk confectioner’s sugar, vanilla, simple syrup for Rosemary Glaze. Drizzle all over cake and garnish.
Serve with tea or coffee and enjoy!