Preheat oven to 350°F (175°C). Butter or lightly oil a 9-inch cake pan.
In a medium-sized bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In the bowl of an electric mixer fitted with a whisk attachment, beat the sugar, eggs, and lemon zest until thick, fluffy, and pale, about 3-4 minutes. Add the chopped rosemary. Slowly pour in the olive oil with the mixer running on high. Beat until combined, about 2 minutes.
Reduce speed to low and add the milk and lemon juice alternately with the dry ingredients, mixing just until incorporated.
Pour the batter into the prepared cake pan. Scatter the remaining ½ tablespoon of non-chopped rosemary on top.
Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean (a few crumbs are okay).
Place the pan on a cooling rack and let the cake cool in the pan for 10 minutes. Remove the cake from the pan and allow it to cool completely on the rack.
Once cooled or before serving, dust with powdered sugar and top with mascarpone whipped cream or lemon icing, if desired.
For the Mascarpone Whipped Cream:
In the bowl of an electric mixer fitted with the whisk attachment, whip the cold heavy cream, powdered sugar, and vanilla extract on high speed until soft peaks form.
Add the mascarpone cheese and continue whipping until stiff peaks form. Spread on top of the cooled cake or serve alongside individual slices.