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 softening, 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, the parmesan rind, 1 teaspoon 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, then return to the pot. (Alternatively, partially puree the soup in the pot with an immersion blender.)
Stir 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 stir in the grated parmesan. Top each serving with the remaining 1 tablespoon olive oil and more parmesan.