Heat oil in a saucepan over medium-high heat. Add mushrooms and garlic; sauté 5 minutes. Stir in parsley, wine, basil, oregano, peppers, and purée. Partially cover, reduce heat to medium-low; simmer 30 minutes. Remove from heat.
Arrange the eggplant slices in a single layer on a baking sheet coated with cooking spray. Bake at 400° for 30 minutes, turning the slices over after 15 minutes. Remove from baking sheet, and let cool. Cut the eggplant slices into 1/2-inch pieces, and set aside.
Combine 1/4 cup Parmesan cheese and ricotta cheese; stir well, and set aside.
Spread 1/2 cup tomato mixture in the bottom of an 11 x 7-inch baking dish coated with cooking spray. Arrange 1 1/2 slices matzo over tomato mixture, and top matzo with half of ricotta cheese mixture, half of eggplant, and half of tomato mixture. Repeat the layers, ending with the tomato mixture. Sprinkle with remaining 2 tablespoons of Parmesan cheese.
Cover and bake at 350° for 45 minutes. Uncover and bake an additional 15 minutes. Let stand 5 minutes before serving.