Wash the fresh broccoli thoroughly under cold water and chop into small florets, discarding tough stems.

Heat olive oil in a large pot over medium heat. Add diced onion and sauté for 5 minutes until translucent.

Stir in minced garlic and sauté for an additional minute until fragrant.

Add diced potatoes and sliced carrots, stirring to combine and cook for 5 minutes.

Pour in vegetable broth and bring to a gentle boil. Add reserved broccoli florets, salt, and pepper.

Reduce heat to low, cover the pot, and let the soup simmer for 15-20 minutes.

Blend the soup using an immersion blender until creamy.

Return blended soup to pot and adjust thickness with additional broth or water as necessary.

Ladle into bowls and garnish with Parmesan cheese, red pepper flakes, and parsley.