Heat the olive oil in a large pot or Dutch oven over medium heat.
Add the chopped onion and garlic, sautéing for about 4 minutes until softened and fragrant.
Add the sliced carrots and celery and cook for another 5 minutes, stirring occasionally, until they begin to soften.
Stir in the crushed tomatoes and thyme sprigs, cooking for 2 minutes more to meld the flavors.
In a small bowl, mash ½ cup of the rinsed chickpeas with the back of a fork until a rough paste forms.
Add this paste, the remaining whole chickpeas, vegetable broth, and 2 cups (480 ml) of water to the pot. Increase the heat to bring the soup to a boil, then reduce to a medium-low simmer for 5 minutes.
Stir in the ditalini pasta and chopped basil, and cook for 7-8 minutes, or until the pasta is al dente, stirring occasionally.
Check the soup's consistency; add a splash more broth or water if it has become too thick.
Season generously with salt and pepper to taste. Carefully remove and discard the thyme sprigs before serving. Ladle into bowls and garnish with fresh, thinly shredded basil.