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.
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.
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.
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
Spread the topping directly onto the shells in Step 4, no prebaking required.