Salt eggplant and drain on paper or kitchen towels 20 minutes. Pat dry.
For the Tomato-Basil Sauce: Heat oil over medium-low heat and melt butter. Add onions and garlic, and cook covered until very soft, 8-10 minutes, stirring occasionally. Raise heat a bit and add stock, tomatoes and passata. Bring to a bubble, break up tomatoes and add basil. Simmer uncovered for 30 minutes; season with sea salt to taste.
Assemble the Parm: Combine breadcrumbs, cheese, lemon zest and herbs in a shallow dish. Pour flour into a second dish and beat eggs in a third.
Season pounded chicken cutlets with salt and pepper. Form a sandwich with 1 eggplant slice, 2 slices mozzarella and 1 chicken cutlet, covering the cheese completely. Coat the sandwiches with flour, egg then breadcrumbs.
Heat oil, about 1/4 inch, for shallow frying over medium to medium-high heat. Fry sandwiches 2 at a time until cooked through and deeply golden, 8-10 minutes, turning occasionally. Keep warm on rack set over baking sheet in warm oven at 275˚F. Repeat with remaining sandwiches.
Raise oven heat to 375˚F.
Spread some sauce in a casserole dish and shingle in sandwiches. Top with a little more sauce and sprinkle with remaining Parm; bake until golden.
Cook some spaghetti to al dente or char some bread to pass at the table. If you make the spaghetti, drain it and toss with a cup of reserved starchy water, some tomato sauce, butter and extra cheese. Pass remaining sauce to tables with stuffed eggplant and chicken parm.