In a medium saucepan, cook the orzo in plenty of boiling salted water for about 5 minutes. Drain and reserve. (If you are using pastina, cook it according to the directions on the package.)
Peel, trim, and finely dice the onion. Peel, trim, and thinly slice the garlic. Peel, trim, and dice the carrots into cubes. Peel the turnips, cut into thin slices, and cut the slices in half. Wash, trim, and slice the zucchini into thin rounds. Wash, trim, and quarter the mushrooms.
In a large heavy pot, sauté the onion in the olive oil over moderate heat, stirring, until translucent. Add the garlic and sauté it, taking care that it does not brown. Add the carrots, turnips, zucchini, and mushrooms, and sauté for 1 minute. Cover the pan, reduce the heat to low, and sweat the vegetables for 10 minutes.
Add the broth, thyme, salt, and pepper and simmer the soup for 30 minutes. 5. Add the broccoli to the soup and cook for 5 minutes. Add the peas and cook for 2 minutes more. Taste and correct the seasonings.
Stir in the reserved orzo and bring the soup to a boil. Add the chopped tomatoes and parsley, stir to combine well, and serve immediately.