Heat olive oil in a large pot over medium heat. Add onion and cook until softened, about 5 minutes. Add garlic and cook for 1 minute more.
Add crushed tomatoes, chickpeas, vegetable broth, smoked paprika, and cumin to the pot. Bring to a boil, then reduce heat and simmer for 20 minutes.
Use an immersion blender to blend the soup until smooth. Alternatively, carefully transfer the soup to a regular blender and blend until smooth (blend in batches if necessary).