In a large pot, heat olive oil over medium heat. Add the chopped onion and sauté for 3-4 minutes until it’s soft and translucent. Stir in the minced garlic and cook for another minute until fragrant.

Add the broccoli florets and vegetable broth to the pot. Bring the mixture to a boil, then reduce the heat and let it simmer for about 10-15 minutes, or until the broccoli is tender.

Using an immersion blender, puree the soup until smooth. If you don't have an immersion blender, carefully transfer the soup to a countertop blender, blend in batches, and return it to the pot.

Stir in the heavy cream and let the soup warm through. Gradually add the shredded cheddar cheese, stirring constantly until melted and creamy.

Taste the soup and add salt and pepper to your liking. Serve hot, garnished with croutons or a sprinkle of fresh chives.