Heat olive oil in a large saucepan over medium heat. Add onion and garlic and cook, stirring for 2 minutes or until onions have softened but not browned.
Add mince and cook, stirring until browned and broken up, about 7 minutes.
Add carrot, mushrooms and celery and cook, stirring for a further 2 minutes. Then add remaining ingredients and stir to combine. Bring to the boil, cover and reduce heat to medium-low. Simmer gently for 20 minutes.
While mince is simmering prepare pasta according to directions on the packet. Drain and combine with savoury mince.
Pour mince mixture into a large baking dish. Push bocconcini halves into the mixture, then sprinkle with cheese. Bake in preheated oven for 20 minutes or until cheese has melted and browned.