Finely dice the garlic and onions. Clean and grate the zucchini.
Heat two tablespoons of oil in a pan. Fry the minced meat in it for about 4 minutes. Add another tablespoon of oil, sauté the garlic, onions and zucchini for 2 minutes. Season the mince mixture with salt, pepper and 1 tablespoon of thyme leaves and let cool down briefly.
Preheat the oven to 180 ° C.
Grease a baking dish with 1/2 tablespoon oil. Fill the cannelloni with the mince mixture and place in the mold. Bring the milk and broth to the boil in a saucepan, thicken with roux and pour over the pasta. Rub the cheese evenly over the casserole.
Bake the cannelloni on the middle rack for 35-40 minutes until golden brown. If the cheese gets too dark shortly before the end of the cooking time, cover with aluminum foil.