Start by preparing your vegetables. Finely chop the onion, celery, and carrot. Peel and cut the potato into 1-inch cubes. Halve the zucchini lengthwise and slice it into "half moons." Finely chop the garlic and parsley.
Heat the olive oil in a stockpot or Dutch oven over medium-high heat. Add the onion and garlic and sauté for about 2 minutes.
Add the chopped celery and carrots and cook for another 2 minutes, stirring often, until they begin to soften.
Stir in the tomato purée, cumin, red pepper flakes, turmeric, and smoked paprika. Cook for 2 more minutes, stirring, until the spices are fragrant.
Add the diced tomatoes, potatoes, and zucchini to the pot.
Pour in the vegetable broth and give everything a good stir. Reduce the heat to low and let the soup simmer for about 40 minutes, or until the potatoes are fork-tender.
Add the fresh spinach and stir it into the soup. Allow it to wilt for about 1 minute before serving.
Serve the soup hot, garnished with a sprinkle of fresh chopped parsley.