Prepare the Vegetables: Sprinkle salt over the sliced zucchini and eggplant. Let them sit for 10 minutes, then pat dry with a paper towel to remove excess moisture.
Sauté the Aromatics: Heat vegetable oil in a pan over medium heat. Sauté the onion and garlic until soft and fragrant.
Cook the Vegetables: Add the carrot, bell pepper, and mushrooms. Cook for 5 minutes, stirring occasionally.
Add Tomatoes and Simmer: Stir in the diced tomatoes and let them simmer until softened.
Combine Everything: Add the zucchini and eggplant to the pan, mixing well. Cook for another 5 minutes.
Add the Cream and Cheese: Pour in the milk cream, season with black pepper and salt, and let it simmer for a few minutes. Stir in the grated Parmesan cheese until melted and fully combined.
Garnish and Serve: Remove from heat and sprinkle with fresh parsley. Serve warm with crusty bread, pasta, or as a side dish.