Preheat the oven to 185 °C (365 °F).
Cut the tops off the tomatoes (like 'hats') and carefully scoop out the pulp with a spoon. Chop the pulp. Similarly, hollow out the zucchini.
Rinse the rice thoroughly and let it drain. Mix the ground meat with the chopped onion, garlic, rice, parsley, and mint.
Add half of the chopped tomato/zucchini pulp. Mix the mixture thoroughly by hand and season generously with salt and pepper.
Stuff the vegetables with the meat mixture. Do not fill them all the way to the top, as the rice will expand. Optionally, cover with the tomato 'hats'.
Pour the rest of the chopped pulp into the baking dish. Mix the tomato paste with water/broth and a little olive oil, and pour this sauce into the bottom of the baking dish.
Place the stuffed vegetables in the sauce and drizzle the tops with the remaining olive oil.
Bake for approximately 70-80 minutes at 185 °C (365 °F) until the vegetables are soft and the rice has absorbed all the liquid. You may add a little more water during baking if necessary.