Preheat the oven:
Preheat your oven to 375°F (190°C). Place potato wedges in a 9×13 baking dish. Toss with 1 tablespoon of olive oil, salt, and pepper, and roast for 15-20 minutes. Set the baking dish aside but leave the oven on.

Prepare the tomatoes:
Cut the top quarter off each tomato and set the tops aside. Use a paring knife to loosen the core and pulp, then scoop it out carefully with a spoon, being careful not to pierce the tomato shells. Transfer the pulp to a bowl and blend until smooth. Lightly salt the inside of each hollowed tomato and place them upside down on paper towels to drain while you prepare the rice.

Cook the rice filling:
In a medium skillet, heat 2 tablespoons of olive oil over medium heat. Add the diced onion with a pinch of salt, and sauté until softened, about 3 minutes. Add the garlic and cook for another minute. Stir in the rice and cook for 2-3 minutes, stirring frequently, until lightly toasted and coated in oil.
Add the blended tomato pulp and ⅓ cup of water or broth to the pan. Bring to a gentle simmer and cook for about 12 minutes, stirring occasionally, until the rice is softened but still underdone. Remove from heat and stir in the chopped basil and Parmesan. Taste and adjust seasoning with salt and pepper.

Stuff the tomatoes:
Arrange the hollowed-out tomatoes on top of the partially roasted potatoes in the baking dish. Loosely fill each tomato with the rice mixture, then place the tops of the tomatoes back on. Drizzle the tomatoes and potatoes generously with the remaining 2 tablespoons of olive oil.

Bake the stuffed tomatoes:
Return the dish to the oven and bake for 40 to 45 minutes, or until the tomatoes are soft, wrinkled, and the rice is fully cooked. For a more caramelized finish, broil for the last few minutes.

Rest and serve:
Let the tomatoes cool slightly, then garnish with a little more chopped basil just before serving. These stuffed tomatoes are delicious both warm or at room temperature.