Preheat the oven to 350 degrees F. Grease a 9" springform pan and set aside.

Whisk the flour, corneal, baking powder, baking soda, salt and 1 cup sugar in a large bowl.

In another bowl, whisk the buttermilk, eggs, and melted butter.

Stir the wet ingredients into the flour mixture until everything is just moistened. Spoon into the prepared pan. Press the pears gently into the surface of the batter.

Bake for 45 to 55 minutes, until the top is golden and a toothpick inserted in the center comes out clean. Allow to cool on a wire rack to 15 minutes before removing the pan and cooling completely.

While the cake cools, make the rosemary simple syrup (make this ahead of time if needed - you'll want to spoon it on while the cake is still warm).

In a small saucepan combine the 1/4 cup water with the remaining 1/4 cup sugar. Add the rosemary sprigs and cook over medium heat. Stir until the sugar is dissolved. Remove from heat and allow to sit for at least 30 minutes.

Remove the rosemary sprigs and brush over the still warm cake.

Slice and serve.