Sauté aromatics: Heat olive oil or vegan butter in a pot over medium heat till oil shimmers. Add red pepper flakes (optional), diced onion, diced celery (optional), sliced carrot (optional), and minced garlic, and sauté for 3-5 minutes, until onions are translucent.
Cook the tomato paste: Add in sun-dried tomatoes, paprika, and tomato paste. Stir, breaking up the tomato paste to coat the aromatics, and sauté for another 2-3 minutes, until the tomato paste darkens to a rusty color.
Add broth + chickpeas: Add in vegetable broth to deglaze, scraping up anything sticking to the bottom of the pan. Add in chickpeas, Italian seasoning, and salt. Bring this up to a boil.
Add pasta: Stir in the orzo and reduce heat to medium-low, or as needed, to establish a rapid simmer. Allow the pasta to cook for about 10 minutes, or until it's almost done but still quite al dente (with a bit of chew in the center). Make sure to stir often to keep it from sticking to itself or the bottom of the pot.
Add kale: Stir in the chopped kale. Keep simmering the soup for about another 5 minutes, until both the kale and pasta are tender. (If you're substituting spinach instead of kale, you can add it a little closer to the end since it's less hearty.)
Finishing touches: Stir in the coconut milk (or other nondairy cream of choice), along with the vegan parmesan and fresh basil. Season with extra salt and pepper to taste.
Enjoy: Serve with extra vegan parmesan and fresh basil. Goes great with a side of crusty bread.