Preheat oven to 200ºC.
Bring a pot of water to the boil (approximately 2/3 full).
Peel and chop the potatoes and sweet potatoes into 2cm chunks. Cook in boiling water for approximately 20-25 minutes until soft.
While potatoes and sweet potatoes are cooking, add finely diced onion, carrot, celery and olive oil to a seperate frypan.
Turn on heat to medium-high heat and sauté (stirring occasionally with a wooden spoon) for approximately 5 minutes, until onions are translucent.
Add garlic and cook for a further minute.
Add beef mince and break up meat with the wooden spoon. Allow to brown and cook for approximately 10 minutes.
Finely chop rosemary and parsley, adding to meat mixture along with tomato paste and water (or stock).
Let simmer and reduce for a further 10 minutes. Set aside.
Returning to potatoes and sweet potatoes, drain the water from the pot.
Mash using a potato masher, until relatively lump-free.
Add butter and stir through to combine.
Assemble pie, by placing meat mixture into the bottom of a baking dish.
Top with potato/sweet potato mixture.
Sprinkle grated cheese over the top.
Bake in oven for approximately 25 minutes. Turn on grill function for last 5 minutes to brown on top.