Prepare the soffritto. Peel the carrot and cut it into small cubes, then peel the onion and finely chop it.
Add the olive oil and a pinch of salt to a saucepan, then add the onion and carrot. Cook over medium heat for about 5 minutes, until softened.
Add the ground veal and ground pork, stir well, and cook for another 5–8 minutes, until the meat is browned.
Deglaze with the white wine and let it evaporate over high heat.
Add the tomato passata and stir it together with the other ingredients.
Add the water and a few basil leaves, give everything a good stir, and cook for about 30–40 minutes. The ragù shouldn’t thicken too much, as the sauce will help cook the pasta later. At the end of cooking, let the ragù cool for at least 10 minutes.
Meanwhile, cook the conchiglioni in salted boiling water for 5 minutes. Drain them al dente and place them on a kitchen towel. Turn them upside down so any excess water can drain and be absorbed by the towel.
Spread a layer of béchamel sauce on the bottom of a baking dish, then add 3–4 tablespoons of ragù.
Place the conchiglioni on top, open side facing up.
Spoon the ragù into a piping bag and fill the conchiglioni.
Cover the stuffed shells with the béchamel sauce.
Sprinkle the grated cheese on top.Bake the stuffed shells in a preheated oven—200°C (390°F) for a conventional oven, or 190°C (375°F) for a fan-forced oven—for about 20 minutes. Bring the stuffed shells to the table and serve them hot!