Arrange tomatoes on a large baking sheet, cut-side up. Drizzle with oil and sprinkle with 1/2 teaspoon of salt and 1/2 teaspoon of pepper. Transfer to the oven and roast for about 20 minutes. Set aside to cool.
Decrease oven temperature to 375°F.
In a medium saucepan over medium-high heat, add the olive oil and sauté the sliced onion until soft and opaque, about 3 minutes.
Add the roasted tomatoes, 1 teaspoon of salt, and the oregano and cook for an additional 2 minutes.
Add the vegetable stock and rice and and stir for 2 minutes.
Add salt and pepper to taste and remove from the heat.
Ladle half of the mixture into the baking pan and top evenly with mozzarella cheese. Ladle the rest of the mixture over the cheese and top with the Parmigiano-Reggiano.
Transfer to the oven and bake for 35 minutes or until all the liquid is absorbed.
Remove from oven and let rest for 15 minutes. Invert a serving platter over the baking pan and flip to transfer the cake. Remove the pan and serve.