Heat 3 tablespoons olive oil in a large pot over medium-high heat. Add the garlic and cook, stirring, until golden, about 2 minutes. Add the onion, carrots, and celery and cook, stirring occasionally until the vegetables start to soften, 12 to 15 minutes. Stir in the tomato paste and rosemary and cook until the tomato paste darkens in color, about 3 minutes.

Stir in 6 cups water, the chickpeas with their liquid (if using home-cooked chickpeas, add about 1/2 cup of the liquid), 1 teaspoon of salt and a few grinds of pepper. Bring to a boil, then reduce the heat and simmer until the vegetables are soft, about 10 minutes. Remove 1 cup of the soup (chickpeas, vegetables, and broth) and puree in a blender (or partially puree the soup using an immersion blender), then return to the pot.

Sir the pasta and escarole into the soup. Cook until the pasta is tender and the escarole is wilted about 6 minutes. Remove from the heat and top each serving with a drizzle of olive oil.