Make the tomato sauce: Heat 2 tablespoons of olive oil in a saucepan over medium heat. Add the whole garlic clove and sauté until fragrant, then remove the garlic. Add the tomato purée and cook until the sauce thickens.

Prepare the filling: Clean the eggplant and zucchini, then dice them. Heat 3 tablespoons of olive oil in a skillet over medium heat. Add the chopped onion and sauté until soft. Add the diced vegetables and cook until they are tender. Remove from heat and let cool.

In a bowl, beat the egg. Add the cooled vegetables and the caciocavallo cheese cut into very small cubes. Mix well, season with salt and pepper, and let the mixture rest.

Boil the conchiglioni pasta until very al dente. Drain and transfer them to cold water to stop the cooking.

Assemble the conchiglioni: Spread one-third of the tomato sauce on the bottom of a baking dish. Fill the conchiglioni with the vegetable and cheese mixture and arrange them in the dish. Once all the pasta is filled and arranged, pour the remaining tomato sauce over the top. Bake in a preheated oven at 350°F (180°C) for 40 minutes. Sprinkle with Parmesan cheese and bake under the broiler for another 10 minutes. Serve hot.