Heat olive oil in a large pot or Dutch oven over medium heat. Add the finely chopped onion and sauté for 5-7 minutes until softened and translucent, stirring occasionally.

Stir in the minced garlic and cook for another minute until fragrant, being careful not to burn it.

Add the roughly chopped broccoli florets to the pot. Pour in the vegetable broth. Bring the mixture to a boil, then reduce heat, cover, and simmer for 10-12 minutes, or until the broccoli is very tender.

Carefully use an immersion blender to purée the soup directly in the pot until smooth and creamy. If using a standard blender, work in batches, filling the blender only halfway, and venting the lid to allow steam to escape (cover with a kitchen towel). Return blended soup to the pot.

Stir in the milk and 3/4 of the crumbled feta cheese. Heat gently for 2-3 minutes, just until warmed through, but do not boil after adding milk and feta. Season with salt and freshly ground black pepper to taste. Remember feta is salty, so taste before adding too much salt.

Ladle the hot soup into bowls. Garnish each serving with the remaining crumbled feta cheese and a grind of black pepper. A squeeze of fresh lemon juice before serving can add a bright finish, if desired.