01 - Melt butter in a large pot over medium heat. Add diced onion, carrot, and celery. Sauté for 5 minutes until vegetables are softened and fragrant.
02 - Stir in minced garlic and cook for 1 minute until aromatic. Add flour and cook, stirring constantly, for 2 minutes to form a smooth roux that will thicken the soup.
03 - Gradually whisk in vegetable broth, ensuring no lumps remain. Add chopped broccoli, dried thyme, ground nutmeg, salt, and black pepper. Stir to combine.
04 - Bring mixture to a simmer, cover pot, and cook for 15 to 20 minutes until broccoli is completely tender and can be easily pierced with a fork.
05 - Use an immersion blender to puree the soup directly in the pot until completely smooth. Alternatively, transfer soup in batches to a stand blender, puree, then return to pot.
06 - Reduce heat to low setting. Stir in whole milk and heavy cream until incorporated. Gradually add grated sharp cheddar cheese, stirring continuously until fully melted and soup is silky smooth.
07 - Taste soup and adjust salt and pepper seasoning as needed. Serve hot in bowls, garnished with additional shredded cheddar cheese or fresh herbs if desired.