Pat dough into a 12-inch pizza pan coated with cooking spray. Bake at 425° on bottom rack of oven for 5 minutes.
Place portobello mushrooms in a large nonstick skillet; add 1/4 cup wine. Bring to a boil; cover, reduce heat, and simmer 10 minutes or until mushrooms are tender. Remove from skillet; set aside. Wipe skillet dry with a paper towel.
Coat skillet with cooking spray; add oil. Place over medium-high heat until hot. Add garlic, 4 ounces sliced fresh mushrooms, and shiitake mushrooms; saute until tender. Add remaining 1/2 cup wine. Bring to a boil; reduce heat, and simmer, uncovered, until liquid evaporates.
Position knife blade in food processor bowl; add shiitake mushroom mixture, Parmesan cheese, lemon juice, and olives. Process 10 seconds or until almost smooth.
Spread shiitake mushroom mixture over crust, leaving a 1/2-inch border. Arrange portobello mushrooms over mushroom mixture; sprinkle with Swiss cheese. Bake at 425° on bottom rack of oven for 12 minutes or until crust is lightly browned and cheese melts. Remove from oven, and sprinkle with basil. Let stand 10 minutes before serving.