Cut 6 slits into each eggplant being careful not to cut all the way through. It will look like an armadillo. Salt the flesh of the eggplant and let stand 30 minutes. Pat the moisture away with paper towels.

Meanwhile, heat olive oil, 2 turns of the pan, in a medium saucepot. Add butter and melt it into oil. Add garlic and swirl 2 minutes then spoon off a few tablespoons and moisten the panko. To the pot, add halved onion, bay, tomatoes, crushing them up a bit. Add a few sprigs thyme, stir in stock and honey or sugar, and tear in a few leaves of basil. Simmer 20 to 30 minutes. Remove thyme stems, bay and onion. Season with salt and pepper, to taste.

Preheat oven to 400F.

Fill the accordion folds of the eggplants with slices of mozzarella. Choose casserole dishes that leave some room around the eggplants. Divide the sauce between the casseroles, arranging 2 eggplants in each. Cover casseroles with foil and roast 20-30 minutes. Remove the foil and cook until eggplant is crispy at edges, about 20-30 minutes more.

Toss the garlic-butter panko with cheese, chopped parsley and mint. Once eggplant is crispy at edges, top with breadcrumbs, return to oven to brown, 10-15 minutes more.

Serve whole eggplant with sauce per person and garnish with a few leaves of torn basil.