Cake: Preheat oven to 350 degrees. Brush a 10-inch Bundt pan with 1 tablespoon butter. Sprinkle with 2 teaspoons rosemary and 2 tablespoons polenta; shake to coat.
Whisk together flour, baking powder, salt, and remaining 3/4 cup polenta and 4 teaspoons rosemary. In another bowl, whisk together oil, eggs, yolks, and vanilla.
Beat remaining 1/2 cup butter and the sugar on medium until pale and fluffy, about 3 minutes. Slowly beat in egg mixture until just combined. With mixer on low, add flour mixture in 3 batches; beat until just combined.
Pour batter into pan. Bake until golden and a toothpick comes out clean, 35 to 40 minutes. Let cool in pan 15 minutes, then turn out onto a wire rack to cool completely.
Glaze: Whisk together all ingredients until smooth. Drizzle glaze over cake. Cut into wedges; serve.