1. Heat the oven to 425°. Oil two 12-inch pizza pans or large baking sheets. Press the dough into a 12-inch round, or 9-by-13-inch rectangle, on each prepared pan. Bake until the dough begins to brown, 10 to 15 minutes.
2. Meanwhile, in a large nonstick frying pan, heat 1 tablespoon of the oil over moderately high heat. Add the zucchini and cook, stirring occasionally, until almost tender, about 3 minutes. Transfer to a small bowl. Heat the remaining 2 tablespoons of oil in the same pan. Add the mushrooms, salt, pepper, and thyme and cook, stirring frequently, until the mushrooms are golden, about 5 minutes.
3. Return the zucchini to the pan, add the wine, and simmer, stirring occasionally, until the vegetables are tender and all the wine has evaporated, about 5 minutes more.
4. Spread the vegetable mixture on the partially baked pizza crusts. Sprinkle each with Swiss cheese and Parmesan and bake until the cheese melts, about 10 minutes.
Wine Recommendation: Nebbiolo is the grape of great Italian wines such as Barolo and Barbaresco. You can enjoy its complex mushroom, spice, rose-petal, and strawberry flavors in a much less expensive Nebbiolo delle Langhe or Nebbiolo d'Alba.
Notes: If you prefer to use store-bought pizza shells, such as Boboli, simply start this recipe with Step 2. Spread the topping directly onto the shells in Step 4, no prebaking required.