Bring the broth, 2 1/2 cups water, butter and 1 teaspoon salt to a boil in a heavy, large saucepan over high heat. Gradually whisk in the polenta. Continue to whisk until the polenta begins to thicken, 2 to 3 minutes. Reduce the heat to low. Cover and cook until the polenta is very thick and tender, stirring often with a flat-bottom spoon or heatproof rubber spatula to prevent sticking or burning, about 20 minutes. Blend the corn in a mini processor until a coarse puree forms. Stir the corn puree into the polenta. Season with more salt if desired.
