Soak dried mushrooms in boiling water for 10 minutes.
Meanwhile whisk together vegetable broth and cornmeal, in a large microwaveable bowl. Cover with wax paper; microwave at high 4-5 minutes. Whisk well; Cook at high 3-4 minutes or until the polenta is thick. Set aside.
Heat oil in large nonstick skillet. Add shallots, cook 3-4 minutes add mushrooms and garlic. Cook another 3-4 minutes, add in tomatoes and pepper flakes. Drain off dried mushrooms add in reconstituted mushrooms a little of their broth. Boil over high, reduce to medium. Simmer uncovered for 5 minutes. Stir in basil.
Spoon polenta on to plates and top with mushroom mixture. Sprinkle with cheese.