Soft Polenta With Sweet Tomato Sauce

Ingredients

• 7 1/2 cups cold water
• 1 tablespoon salt
• 1 1/2 cups coarse cornmeal
• 1 cup fine cornmeal
• 3 tablespoons butter
• 1/4 cup heavy cream
• 1/2 cup olive oil
• 3 pounds tomatoes, halved, seeded and cut into 1/2 inch pieces
• 1 large onion, sliced
• 2 celery stalks, sliced into 1 inch pieces
• 2 medium carrots, peeled and sliced into thin pieces
• 1/2 cup fresh parsley, roughly chopped
• 1/2 cup fresh basil leaves, roughly chopped
• 1 tablespoon butter
• salt
• 3/4 cup freshly grated parmesan cheese, plus more for garnish
• basil sprigs for garnish