Slice the tops off the tomatoes (keep the tops, though) and use a spoon to empty out the middle of the tomato. Reserve the juice in one bowl and insides of the tomato in a separate bowl. Make small slits in the inside bottom of the tomatoes making sure not to cut all the way through the tomatoes.
Lightly grease a 9×13 baking dish and place the tomatoes inside the pan.
Put the onion, garlic, a teaspoon of oil, and a pinch of salt into a food processor and pulse until veggies are slightly broken down and chunky.
Take the insides of the tomato and chop them into small pieces, and then add them to a large bowl with the grated zucchini. Then, add 1 tablespoon of salt, the dry mint, parsley, and tomato paste and combine. Finally, add the uncooked short-grain rice, 1 teaspoon of lemon juice, and 3/4 cup olive oil and let the mixture sit.
In the meantime, peel the potatoes and cut them into chunks. Toss them with the tablespoon of oregano, 3/4 cup olive oil, and some salt and pepper. Mix them well and then add the reserved tomato juice.
Fill the tomatoes to the top with the rice mixture and top them with their caps. Then, place the potatoes/tomato juice in the empty space around the tomatoes also add any leftover rice mixture in the gaps, too.
Add a cup of water to the corner of the pan and tilt it so that the water is evenly distributed.
Bake for 15-20 minutes at 400 degrees F, and then reduce the heat to 325 degrees F and bake them for another 60-90 minutes. If it seems dry during the process, add a little more water to the pan.