Cut the zucchinis in half. Carefully hollow them out leaving an 1/8-inch rim around the zucchini and about 1/2 inch on the bottom (use a dull butter knife or apple corer). Set the hollowed zucchinis to the side.
In a pot large enough for all the zucchinis to fit, heat the olive oil over medium heat and add the onion, tomatoes, and garlic. Stir occasionally for 5 minutes, simmering on medium-low. Add the salt, pepper, tomato paste and vegetable broth. Allow to simmer over low heat while you stuff your zucchini.
Prepare the filling: in a large bowl combine the beef, rice, parsley, mint, salt, pepper, and allspice and stir well.
Fill each zucchini 3/4 of the way full, be careful not to over stuff because the rice will expand.
Once all the zucchini are stuffed lay them down over the onions and tomatoes in the pot. Cover with water, turn the heat to medium-high and bring to a boil. Once at a boil reduce the heat to low and simmer, covered, for 1 hour.
After an hour check and make sure the rice is cooked. If the rice is under-cooked cover the pot and simmer for 10-15 minutes longer. Once the rice is tender turn off the heat and allow to sit for 15 minutes.
Serve the zucchini with the tomato sauce and top with yogurt. Sprinkle with the reserved 1 TBSP fresh chopped parsley and 1 tsp chopped mint.