Heat the olive oil in a large pot over medium heat. Add the diced onion and cook until translucent, about 4-5 minutes.

Stir in the minced garlic and cook for an additional minute, until fragrant.

Toss in the broccoli florets and pour in the vegetable broth. Bring the mixture to a simmer, then cover and cook for about 10 minutes, or until the broccoli is tender.

Using an immersion blender, puree the soup until smooth. If you don’t have one, you can transfer the mixture carefully to a regular blender in batches.

Return the blended soup to low heat and stir in the milk and shredded cheddar cheese. Mix until the cheese melts completely, creating a creamy consistency. Add salt and pepper to taste.

If you’re using chicken or turkey, fold it in now and allow it to warm through.

Ladle the soup into bowls and garnish with your favorite toppings, perhaps some more cheese or croutons!