In a large pot over medium heat, add 2 tablespoons olive oil. Add onion and cook until soft (about 5 minutes. Add the 2 cloves of garlic and cook, stirring until it softens but doesn't brown.
Stir in the tomato paste, salt, and pepper and cook with the onion/garlic mixture for about a minute.
Add the chickpeas and water and bring to a boil. Once the water has come to a boil, add in pasta, lower the heat, and simmer until the pasta is cooked, about 10 minutes (NOTE: if you are using the cheese rind, you should tuck it into your soup pot here and let it cook with the pasta). Depending on how "soupy" or "stewy" you like your dish, you can add additional water here (just remember to re-season)
Once the soup is done (when the pasta is tender), heat the remaining 1/4 cup olive oil in a small pan over medium-low heat, add remaining 2 cloves of garlic, a pinch of pepper flakes and cook until the garlic almost begins to colour. Pour this over the soup and stir well (if the original garlic, that is a large piece, bothers you, you can fish that out here).
Remove the parmigiano rind (if using), taste (see post for ideas on what to do with the rind), adjust seasoning if necessary and ladle soup into bowls. Serve immediately.