How to Make It
Heat oven to 350° F. Butter a 9-inch springform pan.
Whisk together the flour, cornmeal, baking powder, baking soda, salt, and 1 cup of the sugar in a large bowl. Whisk together the buttermilk, eggs, and melted butter in a medium bowl. Add the wet ingredients to the dry ingredients and whisk to combine. Fold in the pears.
Transfer the batter to the prepared pan. Bake until a toothpick inserted in the center comes out clean, 45 to 55 minutes. Cool in the pan for 15 minutes; transfer to a wire rack.
Meanwhile, heat the rosemary, the remaining ¼ cup of sugar, and ¼ cup water in a small pot over medium heat. Cook, stirring, until the sugar is melted. Remove from heat, cover, and let sit, stirring occasionally, for 30 minutes and up to 4 hours. Discard the rosemary sprigs.
While the cake is still warm, brush the top and side with the rosemary syrup.
Serve warm or at room temperature with whipped cream, if desired.