Wait for the liquid to evaporate, add the zucchini and mushrooms, braise them too, then add the peppers. Season to taste with the spices, cook another 5 min. and take the pan off the stove. Leave it to cool.
To make the Bechamel, put a casserole on the stove, add the butter to it and once it melts, add the flour, braise briefly while stirring nonstop. Pour in the heated milk and boil the sauce until thickened while stirring, so it doesn't stick to the bottom. Season with salt, nutmeg and ground white pepper.
In the tray you'll be baking in, pour on half the tomato sauce, grate a garlic clove and sprinkle with basil. Pour on a ladle of Bechamel sauce and spread it out evenly.
Fill the cannelloni with the meat mixture - take each cannelloni, use your hand to plug one of its ends and fill it up to the top from the other end using a spoon or even better, your fingers. Stuff the cannelloni well with the mixture. Arrange them in the tray next to one another, pour the remaining tomato sauce over them and all of the Bechamel.
Cover the tray with aluminum foil and bake in a 356°F (180 °C) oven for about 20 min. Take the foil off and grate cheese generously over the cannelloni.
Return to the oven to bake until the cheese gains a golden crust - about 15 min. Finally, take the tray out and wait for them to cool a bit. Consume warm but not hot.