Preheat the oven to 180°C (160°C fan) / 360°F.
Prepare the eggplant: cut into cubes, or slice each eggplant in half lengthwise and lightly score the flesh.
Arrange the eggplant pieces or halves on a baking tray; add the garlic clove (if using), drizzle generously with olive oil, then season with sea salt and black pepper.
Roast in the oven for about 20 minutes, until the eggplant is soft and cooked through.
Transfer the roasted eggplant (and garlic, if used) to a food processor and blend until smooth and creamy.
Bring a large pot of lightly salted water to a boil. Briefly cook the cannelloni tubes for 1–2 minutes until still quite firm, then drain and pat dry on a kitchen cloth or paper towel.
Fill a piping bag with the roasted eggplant mixture, then carefully pipe the filling into each cannelloni, holding the tube over your palm to support it and prevent spillage.
Brush the base of a baking dish with a little olive oil and spread some of the tomato sauce over the bottom.
Arrange the filled cannelloni in the dish, spoon the remaining tomato sauce over them, then top with the béchamel sauce and sprinkle the grated Italian-style hard cheese on top.
Bake in the oven for 15–20 minutes, until the pasta is cooked through and the edges are slightly crispy.
Scatter fresh basil leaves over the top and serve immediately.