Preparation

Make the syrup

• Finely zest the oranges (for about 1 packed Tbs.), and reserve for the cake batter. Using a knife, shave off the oranges’ skin and white pith. Over a small bowl, cut between the membranes to remove the segments, dropping them into the bowl. Squeeze the juice from the membranes, and add to the segments (about 3/4 cup total). Set aside.
• Combine 1/3 cup water, the sugar, and rosemary in a small saucepan. Bring to a simmer, stirring occasionally, until the sugar dissolves, about 4 minutes. The syrup will be fluid, not thick. Remove from the heat, and stir in the reserved orange juice and segments. Let cool to room temperature.

Make the cake

• Position a rack in the center of the oven, and heat the oven to 325°F. Lightly grease a 9-inch cake pan with oil, fit the bottom with a piece of parchment, and oil the parchment.
• In a medium bowl, whisk the flour, cornmeal, baking powder, baking soda, and salt. In a stand mixer fitted with the whisk attachment (or in a large bowl using a hand mixer), beat the 3/4 cup oil, sugar, eggs, crème fraîche, finely chopped rosemary, vanilla, and reserved zest until well combined, about 1 minute. In three stages, with the mixer on low speed, add the flour mixture to the egg mixture, scraping down the bowl as needed. Whisk just until the batter comes together. It will be very thick.
• Spoon the batter into the prepared pan, and spread the mixture evenly. Lay the sprig of rosemary on the center of the cake. Bake the cake until lightly brown at the edges and a toothpick inserted into the center comes out clean, 30 to 32 minutes. Place the pan on a cooling rack, and cool until slightly warm.
• Run a paring knife around the perimeter of the cake to separate it from the pan. Set a plate on top of the cake, and flip it over (remove and discard the parchment). Then flip the cake back onto the rack, and set it over a rimmed baking sheet.
• Spoon all of the syrup—but not the orange segments—over the cake. Serve the sliced cake topped with a spoonful of the orange segments and a dollop of crème fraîche.