Heat 2 tablespoons of olive oil in a large pot over medium heat. Add diced onion and sauté for 2-3 minutes until translucent and fragrant.

Add chopped celery and sliced carrots to the pot. Sauté for 3-5 minutes, stirring occasionally, until the vegetables begin to soften.

Add diced red bell pepper and cubed potatoes to the pot. Stir well to combine all vegetables. Pour in water or vegetable broth, cover the pot, and bring to a boil. Reduce heat and simmer for 15 minutes.

While the soup simmers, heat olive oil in a separate pan over medium heat. Add sliced mushrooms and sauté until they release their moisture and turn golden brown, about 5-7 minutes.

Add minced garlic, salt, black pepper, and Khmeli-Suneli spice blend to the mushrooms. Sauté for another 2 minutes until aromatic and golden. Transfer the seasoned mushrooms to the soup pot.

Add half of the broccoli florets to the soup and let it simmer for 10 minutes. Meanwhile, bring a small pot of water to a boil and cook the remaining broccoli florets for 2 minutes until just tender. Drain and set aside for the croutons.

In a bowl, coarsely grate or mash the cooked broccoli that was set aside. Mix with grated Parmesan cheese, Greek yogurt or sour cream, salt, and black pepper until well combined.

Spread the broccoli-Parmesan mixture generously on bread slices. Place on a baking sheet and bake in a preheated oven at 180°C / 350°F for 10 minutes until golden and crispy.

Taste the soup and adjust seasoning with salt and pepper as needed. Stir in freshly chopped parsley just before serving.

Ladle the hot soup into bowls. Top with additional fresh parsley and serve alongside the warm broccoli Parmesan croutons.