Begin by heating a large pot over medium heat and adding the butter. Once melted and shimmering, add the diced onion and sauté for about 5-7 minutes until translucent and fragrant, with a slight sweetness in the aroma.
Add the minced garlic to the pot and cook for about 30 seconds until fragrant, stirring constantly to prevent burning.
Stir in the chopped broccoli, coating it with the aromatic mixture, and cook for about 3-4 minutes until the broccoli brightens in color and starts to soften slightly.
Pour in the broth, bringing the mixture to a gentle simmer. Cover and let it cook for 10-15 minutes until the broccoli is tender but still has a slight bite.
Use an immersion blender to carefully blend the soup directly in the pot until smooth or slightly chunky, depending on your preference. If using a regular blender, blend in batches with caution to avoid splashing hot liquid.
Return the soup to low heat and stir in the shredded cheddar cheese, a handful at a time, until melted and silky smooth. Keep stirring to prevent clumping.
Add the heavy cream and stir well to incorporate, warming gently without boiling to maintain a creamy texture and bright flavor.
Season with salt and black pepper to taste, adjusting the flavor until it’s perfectly balanced and vibrant.
Let the soup rest for a few minutes to let flavors meld, then ladle into bowls and serve hot, garnished with extra cheese or pepper if desired.