In a large pot, melt the butter over medium heat. Add the diced onion and cook until translucent, about 5 minutes.

Add minced garlic and cook for another minute until fragrant.

Stir in chopped broccoli and cook for 2-3 minutes.

Pour in chicken broth and bring to a boil. Reduce heat and simmer for 15 minutes until broccoli is tender.

Using an immersion blender, blend the soup until smooth. Alternatively, transfer to a blender in batches and blend until smooth.

Return the soup to the heat, stir in milk and shredded cheddar cheese until melted and creamy. Season with salt and pepper to taste.