Start the stew: Set a large heavy pot or Dutch oven on the stove over medium heat. Add 2 tablespoons of the olive oil and let it warm for about 30 seconds.

Add the chopped onion, diced carrots, and 1/2 teaspoon of the salt to the pot. Cook for 5 to 6 minutes, stirring often, until the onion looks soft and the carrots have started to lose their raw edge.

Add the zucchini to the pot. Cook for 4 minutes, stirring every minute or so, until the zucchini starts to soften but still holds its shape.

Add the 3 minced garlic cloves to the pot. Stir for 30 seconds, just until the garlic smells fragrant.

Add the rinsed lentils to the pot. Stir for 1 minute so the lentils are coated with the oil and vegetables.

Pour the vegetable broth into the pot and add 1/4 teaspoon of the black pepper. Turn the heat to high and bring the liquid to a full boil.

When the broth is boiling, lower the heat to medium-low so the liquid bubbles gently instead of boiling hard. Cover the pot partway with a lid and simmer for 22 to 25 minutes, stirring once or twice, until the lentils are almost tender.

Add the drained chickpeas to the pot. Keep the pot uncovered and simmer for 8 to 10 minutes more, until the lentils are fully tender and the broth has thickened slightly.

Stir together the pistou: While the stew finishes, put the chopped basil, grated Parmesan, the remaining grated garlic clove, 1 teaspoon of lemon zest, and 1 tablespoon of lemon juice into a small bowl.

Add the remaining 1 tablespoon olive oil and 1/4 teaspoon of the salt to the bowl. Stir well until the mixture looks like a loose, spoonable paste.

Finish the stew: Taste the stew in the pot. Add the remaining 3/4 teaspoon salt, or a little more if needed, until the broth tastes well seasoned.

Turn off the heat under the pot. Stir 2 tablespoons of the basil pistou into the stew so the broth picks up some of the herb and cheese flavor.