Remove stalks from mushrooms and cut in halves. Wipe them down thoroughly with a wet cloth. If washed, mushrooms absorb too much water.Pan fry them and set them aside.
Cut eggplants into 1x4-inhes long, diagonal pieces and pan fry them until tender but not mushy. Set aside to toss in the pasta.
Boil 4 to 5 cups water in a large saucepan with 1 tablespoon salt.
When water comes to a boil, add pasta stir and cook for 4 minutes or until al-dente.
Reserve one cup pasta water, and drain pasta in a colander.
While you are cooking the pasta, heat oil and butter in a large skillet.
Add ½ cup onion, garlic and ginger and sauté until onion is soft and cooked down.
Add tomatoes and let them softened stirring on and off. Crush them partly but maintain their integrity.
Add tomato paste and cook to caramelize, about a minute Add salt, pepper, and Kalamata olives.
Add broth or water bring it back to a boil before adding drained pasta to the skillet.
Stir to coat the pasta with the sauce while still on slow heat.
Add lemon zest and juice and mix.
Transfer to a serving bowl and add fried eggplants, grated Parmesan cheese, 1 tablespoon softened butter. Mix well and season to taste.
Scatter fried mushrooms and sprinkle parsley on top to serve.