Heat the olive oil in a large Dutch oven or heavy-bottomed pot over medium heat.
Add the diced onion, carrots, and celery. Cook, stirring occasionally, until the vegetables soften, about 8 minutes.
Add the minced garlic, thyme, cumin, smoked paprika, and cayenne pepper (if using). Cook for 1 minute until fragrant. This step builds your aromatic base.
Add the cubed potatoes, vegetable broth, rinsed chickpeas, diced tomatoes (with juice), and bay leaf to the pot.
Bring the mixture to a boil, then reduce the heat to low, cover, and simmer for 15 to 20 minutes, or until the potatoes are fork-tender.
Remove the bay leaf. For a slightly thicker soup, use an immersion blender to blend about one-third of the soup directly in the pot, or carefully transfer one cup of soup to a regular blender, blend until smooth, and return it to the pot. Stir well.
Season the soup with salt and pepper. Taste and adjust seasonings as needed. If the soup is too thick, add a splash more broth or water.
Ladle the soup into bowls and garnish with fresh parsley before serving.
Notes
For the best texture, use waxy potatoes like Yukon Gold, as they hold their shape better than starchy varieties.