Heat the oil in a large Dutch oven over a medium-high flame. Saute the carrots, onion, and celery until translucent, about 5 minutes. Add the garlic, bay leaf, thyme, and chickpeas. Cook for another 2 to 3 minutes, until the garlic is fragrant.
Pour in the stock and bring to boil over high heat. Return to medium-low, and simmer, partially covered, for 15 minutes, until the veggies are very tender.
Remove the thyme sprigs and bay leaf. Puree half of the mixture, either by transferring it to a blender or food processor, or by running your immersion blender through the soup until about half is smooth.
Stir in the arugula off the heat. Ladle the soup into bowls and garnish with grated Parmesan cheese, a drizzle of olive oil, and crusty French bread.