In a large pot, heat the olive oil over medium heat. Sauté the chopped onion until translucent and fragrant, about 3-5 minutes.

Add the minced garlic and cook for an additional minute.

Stir in the broccoli florets and allow them to mingle with the onion and garlic.

Add the vegetable or chicken broth to the pot. Bring the mixture to a boil, then reduce the heat and let it simmer for 15 minutes.

Once the broccoli is tender, use an immersion blender to puree the soup until smooth.

Pour in the heavy cream and stir to combine.

Gradually mix in the shredded cheddar cheese until melted and fully incorporated.

Season with salt and pepper to taste. Serve hot, garnished with extra cheese or croutons if desired.