Begin by making the broth: Place leeks, carrots, salt, bay leaf, thyme, and tomatoes in a large pot with 4 cups of water. Bring to a boil, then reduce heat and allow to simmer 10-15 minutes.
Strain into a large bowl, pressing down on the vegetables to get as much liquid as possible. Return stock to the pot and discard the vegetables.
Add the chickpeas, pasta, and rosemary to the broth. Bring to a boil, then reduce to a simmer and cook, stirring frequently, until pasta is al dente.
Stir in the spinach and allow to wilt.
Adjust seasoning to taste and serve hot.