01 - Melt butter in a large pot over medium heat. Add onions and carrots, sauté until softened, approximately 5 minutes.
02 - Stir in minced garlic and cook for 1 minute until fragrant, being careful not to brown.
03 - Sprinkle flour over vegetables and cook, stirring constantly for 2 minutes to form a smooth roux and eliminate raw flour taste.
04 - Slowly whisk in vegetable broth, ensuring no lumps form. Bring mixture to a gentle simmer.
05 - Add broccoli florets, salt, pepper, and nutmeg. Cover and simmer for 10-12 minutes until broccoli is fork-tender.
06 - Reduce heat to low. Using an immersion blender, puree until completely smooth, or leave slight texture if preferred.
07 - Stir in whole milk and heavy cream. Warm gently over low heat without bringing to a boil to prevent separating.
08 - Gradually add shredded cheddar cheese, stirring continuously until fully melted and incorporated into a velvety consistency.
09 - Taste and adjust seasoning with additional salt and pepper if needed. Serve immediately, garnished with extra cheddar and fresh herbs.