Preheat a Dutch oven or soup pot over medium heat. While it heats, chop the vegetables, drain any canned vegetables except tomatoes, and measure the spices.
Heat 2 tablespoons of oil in a preheated Dutch oven or soup pot over medium heat. Once the oil shimmers, add the chopped onion, bell peppers, and celery. Cook, stirring frequently, until the onion is softened and translucent, about 6 to 8 minutes.
Add the minced garlic, paprika, savory spice, dried basil, za'atar, and thyme. Cook while stirring until fragrant, about 1 minute. Pour in the broth and water, scraping the pot bottom to deglaze. Add the canned diced tomatoes with their juices and cook for a few more minutes, stirring often. Add the remaining vegetables and stir to combine. Push in the three bay leaves and the star anise.
Increase the heat to bring the mixture to a boil. Cover the pot, then reduce the heat to a gentle simmer.
Simmer covered for 30 minutes. Taste and adjust the spices. Continue cooking until the potatoes and zucchini are softened to your preference.
Remove the pot from the heat and discard the bay leaves and star anise. Stir in the lemon juice and the remaining tablespoon of oil. Taste and adjust the seasoning with more za'atar, pepper, minced garlic, or your preferred spice, being careful as the savory spice can quickly become overpowering. Ladle the soup into bowls and serve.
