Heat the olive oil in a large saucepan set over medium-low heat. Add the onion, celery, garlic and rosemary. Cover with a lid and allow the vegetables to cook down until softened, about 15 minutes, stirring occasionally. The idea is to “sweat” the vegetables rather than browning them. Adjust the heat as needed if your burner runs hot.
Stir in the chickpeas and vegetable broth. Bring to a boil, then reduce heat. Simmer for 20 minutes.
Using a slotted spoon, transfer half of the chickpeas to a bowl. If you have an immersion blender, blend the remaining soup in the saucepan until smooth. Alternatively, allow the soup to cool for 10 minutes, then transfer it to a blender or food processor. Puree until smooth, opening the lid (when the blender is NOT running) to release the steam periodically.
Combine the blended soup and the reserved chickpeas in the saucepan. Add the orzo. Simmer, stirring frequently, until the orzo is tender, 7 to 10 minutes. While cooking, scrape the bottom of the saucepan with a wooden spoon to release any soup that starts to stick. Turn down the hit if it’s sticking too much.
Season to taste with salt and pepper. Stir in the parsley. Serve.
If you prefer a thinner consistency, stir in additional broth or hot water.