Heat the olive oil and butter in a large pot over medium heat.
Add the chopped onion to the pot. Sauté until the onions become translucent, about 2-3 minutes.
Add the chopped zucchini to the pot, stirring well to ensure the vegetables are coated with the oil and butter mixture. Next, introduce the minced garlic cloves and cut broccoli florets.
Pour in the water and add the salt and Italian seasoning. Bring the mixture to a gentle boil, then reduce to low heat. Let it simmer for 15-20 minutes or until the vegetables are tender.
Once the vegetables are cooked, use an immersion blender or transfer the soup in batches to a regular blender or food processor to puree until smooth to your preferred consistency.
If necessary, return the pureed soup to the pot. Stir in the cream and let the soup simmer for an additional 5 minutes.
Finally, add the shredded cheese to the soup, stirring until it’s fully melted and incorporated.
Taste the soup and adjust the seasoning if needed, adding more salt or Italian seasoning to your preference.
Serve hot, garnished with shredded cheese or sour cream if desired. You can also sprinkle with your favorite herb or red pepper flakes. Serve it with crusty bread or pita chips.
Store the soup in an airtight container or resealable freezer bags. If you plan to freeze it, make sure the bags are freezer-safe.