Step 1: In a large pot or Dutch oven, combine the water, vegetable broth, quartered onion, carrot chunks, celery chunks, and smashed garlic cloves.
Step 2: Add the soup base spices: garlic powder, onion powder, bay leaves, sea salt, Italian seasoning, dried crushed thyme leaves, dried parsley, poultry seasoning, sweet paprika, dried rosemary, and black pepper.
Step 3: Bring the mixture to a boil over medium-high heat, then reduce heat to low, cover, and simmer for at least 30-40 minutes, or until vegetables are very tender and the broth is deeply flavorful.
Step 4: Carefully strain the broth through a fine-mesh sieve into a clean pot or large bowl, pressing gently on the solids to extract all liquid. Discard the cooked vegetables and bay leaves.
Step 5: Return the strained broth to the pot over low heat. Stir in the vegan Parmesan cheese, miso (if using), and fresh lemon juice until well combined and the miso has dissolved.
Step 6: Taste the soup and adjust salt and pepper if needed. If desired, you can add more lemon juice for brightness.
Step 7: Serve hot with your preferred cooked small pasta (such as pastina, orzo, or couscous) added directly to each bowl. Garnish with fresh parsley or extra vegan Parmesan cheese if desired.