Bring water and salt to a boil in a large pot over high heat.
Slowly add polenta in a steady stream, stirring continuously with a long wooden spoon.
Lower heat to a gentle boil and continue stirring 30 minutes or until polenta pulls away from the sides and is not gritty. You may need to use more water as it cooks. Use boiling water.
Cover pot with buttered waxed paper and place in a warm-water bath. Polenta stays hot up to 3 hours.
Make sauce: Heat oil in a large skillet over medium-high heat; add onion and cook, stirring occasionally, 10 minutes or until onion begins to carmelize; stir in tomatoes, garlic, and mushrooms, reduce heat to medium-low, and cook, uncovered, 15 minutes; stir in basil, salt, and pepper.
Pour hot polenta onto a clean, unfinished wooden table or a large chopping board, 18 x 18 inches (45 cm x 45 cm), and shape into a thick circle.
Make a 4-inch (10-cm) indent in the center, pour in tomato sauce, and sprinkle with cheese.
• Let cool and then slice into pieces for frying.
• Mix in diced mozzarella or fontina cheese.
• Use half water and half milk to make dish more flavorful.
• Cut into slices, put overlapping in buttered baking pan, drizzle with olive oil, and top with lots of grated Parmiggiano cheese. Bake at 400°F (200°C) until browned.