Bring the water to a boil in a large pot. Add the orzo, stir, lower the heat, cover, and simmer for about 7 minutes, stirring as needed.
While the orzo cooks, combine the basil leaves, garlic, pine nuts, and parmesan in a food processor and whirl until well chopped.
Add the oil in a thin stream to make a smooth paste, scraping down the sides a couple of times as needed. Add salt and pepper to taste. Drain the orzo. Toss it lightly with the teaspoon of olive oil and allow it to cool to room temperature, about 10 minutes.
Meanwhile, cut a hole about 2 inches across in the top of each tomato and remove the core. Scoop out the pulp with a small spoon to leave a 1/2-inch-thick shell. Lightly sprinkle the inside of each tomato with salt and pepper. When the orzo is at room temperature, mix it with the Pesto Genovese and, if using, the cheese cubes. Stuff each tomato with about a cup of filling.
Decorate with olives and/or basil and serve at room temperature.
Serves 6
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