Preheat oven to 350 F. Butter or lightly oil a 9″ pan.
In a medium sized bowl, whisk to combine the flour, baking powder, baking soda, and salt. Set aside.
In the bowl of an electric mixer using a whisk attachment, beat the sugar, eggs, and lemon zest until thick, fluffy, and pale, about 3-4 minutes. Add the chopped rosemary. Slowly add the olive oil with the mixer still running on high. Beat until combined, about 2 minutes. Reduce speed to low, and add the milk and lemon juice alternatively with the dry ingredients.
Pour the batter into the cake pan. Scatter the remaining 1/2 tablespoon non-chopped rosemary overtop. Bake 30-35 minutes or until a toothpick comes out clean when inserted into the center of the cake (a few crumbs are okay).
Place the pan on a rack and cool in the pan for 10 minutes. Remove cake from the pan and allow to cool completely on the rack.
Once cooled or before serving, dust with powdered sugar, mascarpone whipped cream or lemon icing.
FOR THE MASCARPONE WHIPPED CREAM
In the bowl of an electric mixer fitted with the whisk attachment, whip the heavy whipping cream, powdered sugar and vanilla extract on high speed until you have soft peaks.
Add the mascarpone cheese and whip til stiff peaks form. Spread it on top of the cooled cake or serve it alongside individual slices.