In a heatproof bowl, soak the porcini in the 1 cup of lukewarm water until softened, about 20 minutes. Drain the porcini, reserving the soaking liquid. Rinse the porcini, then coarsely chop them.
In a large saucepan, heat the olive oil. Add the onion, celery, carrot, parsley and garlic, cover and cook over low heat until softened, about 10 minutes. Whisk in the tomato paste and the porcini and their soaking liquid, stopping when you reach the grit at the bottom. Simmer over moderate heat until almost all of the liquid has evaporated, about 5 minutes. Add the remaining 5 cups of water, the tomato puree and 1 tablespoon of the basil. Cook for 20 minutes. Add the zucchini and cook until crisp-tender, about 5 minutes. Season with salt and pepper. Stir in the remaining 1 tablespoon of basil and serve with the Pecorino Romano.
One Serving 122 calories, 6.2 gm total fat, 1.46 gm saturated fat.