Dip the chicken in the milk for 10-15 minutes. Heat the olive oil in a frying pan with a non-stick bottom. Add the garlic, onion, chicken and stir. Stew the chicken for 3 minutes on each side.
Add the tomato sauce, mushrooms and black pepper. Cover the dish. Simmer for 15 minutes or until the chicken is ready. Meanwhile, cook the spaghetti according to the instructions, add the broccoli to the same water in the last 2 minutes before removing the spaghetti from the heat.
Crumble the mozzarella over the chicken breasts. Leave on the heat until the cheese melts. Serve the chicken on a plate of spaghetti with broccoli.