Gather all ingredients and set up your cooking station.

In a large pot over medium heat, melt 3 tablespoons of butter. Add the chopped onion, celery, and shredded carrot. Sauté 5 minutes until vegetables soften and become fragrant.

Stir in minced garlic and cook for 1 minute more, taking care not to brown it.

Add the broccoli florets and the remaining 2 tablespoons of butter. Stir until the butter coats the vegetables.

Pour in the chicken or vegetable broth. Bring to a gentle boil, then reduce heat and simmer, uncovered, for 10 minutes or until broccoli is tender.

Use an immersion blender to puree the soup until smooth and velvety.

Return the pot to low heat. Stir in milk, heavy cream, and shredded cheddar cheese until fully melted and creamy.

Season with salt and pepper. Let the soup gently simmer 3–5 minutes more to thicken.

Ladle into bowls and garnish with extra cheddar, a drizzle of cream, or croutons for crunch. Enjoy hot!