To a medium pot, add your pasta water and salt and bring it to a gentle boil.
To a large pan over medium-high heat, add olive oil (or vegetable broth if cooking oil-free), cooked chickpeas, and sea salt (if you're using an unsalted can of chickpeas). Allow it to come to a nice sizzle. Then, once your pasta water is boiling, add the garlic to the pan of chickpeas and place your pan on top of the pasta pot with the boiling water, in lieu of over an open flame. This will ensure that your oil picks up the flavors without burning the garlic. You will see little bubbles start to form after about 15 minutes. Remove the pan from the top of your pasta water pot and add pasta to your pasta water. Cook for 1 minute less than the allotted cooking time on the box to make al dente pasta.
While your pasta is cooking, remove half the cooked chickpeas from your pan and place them in a large and tall container (so you can use an immersion blender). Add 1/4 cup of the pasta water and then, using your immersion blender, blend until smooth. If you don't have an immersion blender, you can place your cooked chickpeas into a large bowl, together with 1/4 cup pasta water and use a potato masher or hand mixer to blend them.
Pour the blended chickpea mixture back in the pan with remaining chickpeas. Once your pasta is finished cooking (1 minute before the instructions say they are done), drain the pasta and place it in the pan with the chickpeas. Using tongs, vigorously stir the pasta into the oil over low heat for about 1 minute. The agitation from stirring the pasta over the heat, together with the fat from the oil, is what will cause everything to come together and make this the creamiest dairy-free pasta ever.
Serve with an extra drizzle of olive oil or a crack of black pepper. I garnished my pasta with a little green onion, just for color, but you can garnish with whatever you like (fresh parsley, basil, oregano, etc.) or nothing!