In a large stockpot or Dutch oven, melt the butter with the olive oil over medium heat.
Add the diced onions and minced garlic, and sauté for about 10 minutes, stirring frequently, until softened and fragrant.
Stir in the tomato paste and cook for another minute until it darkens slightly.
Pour in the vegetable stock, tamari, bay leaf, oregano, basil, thyme, salt, and a generous amount of freshly ground pepper.
Bring the mixture to a rolling boil.
Once boiling, add the cauliflower florets and macaroni to the pot. Return to a boil, then reduce the heat to a steady simmer.
Cook for 15-20 minutes, stirring occasionally to prevent sticking, until both the cauliflower and macaroni are tender but not mushy.
Increase the heat to bring the soup back to a rolling boil. Slowly drizzle in the beaten eggs while stirring continuously.
Continue to stir for about 30 seconds until the egg forms delicate ribbons throughout the soup.
Remove from heat, stir in the fresh parsley, and serve immediately.
Top each bowl generously with grated Parmesan cheese.
