In a medium pot over medium-high heat, combine the rice with enough water to cover by 2 inches. Stir in ½ teaspoon of the salt. Bring to a boil, then reduce the heat to medium-low so the liquid is at a simmer and cook, uncovered, until the rice is al dente, 7 to 9 minutes. If the rice hasn't absorbed all the water, drain it in a fine-mesh strainer, transfer it to a large bowl, and let it cool completely. (To speed up the cooling, spread the rice on a large rimmed baking sheet and refrigerate until cool, then return to the bowl.)

While the rice is cooling, combine the zucchini, celery, bell pepper, olives, parsley, and tomatoes in the bowl of a food processor and pulse several times until everything is about the size of grains of rice. Scrape the sides of the bowl as needed and being careful not to overprocess it to mush.

Add the vegetables to the bowl of rice and toss just to combine—and to break up the rice if it has gotten clumpy when cooling.

In a small bowl, whisk together the lemon juice, aioli, mustard, olive oil, the remaining ½ teaspoon salt, and the ground pepper. (If you'd like, you can do this in the food processor instead, especially if it's a small one—just combine the ingredients in the same bowl you used for the vegetables; no need to clean it.) Pour this over the rice mixture and toss just to combine.

Gently fold in the cannellini beans, being careful not to break them up. Taste and add more salt and pepper if needed.

Serve at room temperature or chill and serve cold.