Set a Dutch oven or other heavy soup pot on the stove over medium heat.

Add the olive oil to the pot and let it warm for about 30 seconds.

Add the chopped onion and diced carrots to the pot. Cook, stirring every minute or two, until the onion looks soft and the carrots begin to soften, about 8 minutes.

Add the sliced garlic and chopped rosemary to the pot. Cook, stirring, until the garlic smells fragrant, about 1 minute.

Add the tomato paste to the pot. Stir it over the heat until it coats the vegetables and darkens slightly, 1 to 2 minutes.

Add the rinsed lentils to the pot. Stir so the lentils are coated with the tomato paste and vegetables.

Pour the vegetable broth into the pot. Scrape the bottom of the pot with a spoon to loosen any bits stuck there.

Raise the heat to high and bring the broth to a full boil.

Lower the heat so the liquid bubbles gently. Partly cover the pot and simmer until the lentils are starting to get tender, about 25 minutes.

Stir the drained chickpeas into the pot.

Keep simmering the stew, partly covered, until the lentils are almost fully tender but still a little firm in the center, 8 to 10 minutes more.

Add the gnocchi to the pot. Stir once so the pieces separate in the broth.