Bring a large pot of water to a boil. Add clementine slices and cook 3 to 4 minutes or until very tender but not falling apart. Carefully remove slices and let drain on paper towels.
Preheat the oven to 350 degrees. Lightly oil a 9-inch cake pan. Line the bottom with a round of parchment paper. Butter and flour the pan and set aside.
In a large bowl, whisk together flour, cornmeal, zest, baking powder, and salt. Set aside.
Beat butter and sugar in the bowl of an electric mixer on high until light and creamy. Add eggs, 1 at a time, and beat well after each addition. Combine milk and vanilla. Reduce speed to low and add flour mixture, alternating with milk mixture, in several additions, beating just until mixed.
Spread batter in the prepared pan. Lay boiled clementine slices on top of cake in several circles. Bake about 45 minutes or until a toothpick inserted in the center of the cake comes out clean. Let cool in the pan on a wire rack. Remove from the pan, cut into wedges, and serve.