Heat the olive oil in a Dutch oven or other large heavy-bottomed pot over medium-high heat. Add the turmeric and 2 tablespoons of the garlic and cook until aromatic, about 1 minute. Add the fava beans and water and bring to a boil. Cover the pot, reduce the heat to low, and simmer, covered, until the beans are completely tender, 30 to 35 minutes.

Meanwhile, in a small bowl, stir together the harissa, canola oil, lemon juice, the remaining 3 tablespoons garlic, and 2 teaspoons salt; set aside.

Transfer the beans and the cooking liquid to a blender, add 1 tablespoon salt, and puree the soup until smooth; you may need to do this in batches.

Return the soup to the pot, taste, and add more salt, if you like.

Serve the soup in individual bowls, garnishing each one with a spoonful of the harissa topping. To make ahead, store the soup and the harissa topping separately in the refrigerator for up to 2 days and reheat the soup before serving.