Preheat the oven to 350, move an oven rack to the bottom third of the oven. Grease an 8″ cake pan. Line the bottom with parchment paper, and set aside.

In a medium mixing bowl, whisk together the cornmeal, cake flour, rosemary leaves, baking powder and salt. Set aside.

In a large mixing bowl, beat together the butter and sugar until light and fluffy with a hand mixer. (Or use a stand mixer fitted with the paddle attachment.) Add the vanilla, eggs, and buttermilk. Mix until all combined, and then mix in the lemon juice and zest. Add the flour mixture to the butter mixture, and mix on low speed until no streaks of flour remain, scraping down the sides of the bowl as necessary.

Pour the batter into the prepared cake pan, and bake on the oven rack in the bottom third of the oven for about 30 minutes, or until a toothpick comes out with moist crumbs. Allow to cool completely.

For the balsamic syrup: Combine the balsamic vinegar and sugar in a small saucepan over medium heat. Bring to a boil, and then reduce to a simmer, stirring occasionally until all the sugar is dissolved and the mixture is thickened – about 10 minutes. Allow to cool, and drizzle over each slice of cake just before serving. The syrup can be made up to 3 days in advance and stored in the fridge – bring to room temp before using.