01 - In a large pot over medium heat, melt the butter. Add the onion and carrot, sautéing for 4-5 minutes until softened.
02 - Stir in the garlic and cook for 1 minute until fragrant.
03 - Sprinkle the flour over the vegetables, stirring constantly for 2 minutes to eliminate the raw flour taste.
04 - Gradually whisk in the vegetable broth, ensuring no lumps remain.
05 - Add the broccoli florets, salt, pepper, and nutmeg (if using). Bring to a simmer and cook for 10-12 minutes, until the broccoli is tender.
06 - Reduce the heat to low. Stir in the milk and cream, gently heating without boiling.
07 - Using an immersion blender, blend the soup to your desired consistency (smooth or slightly chunky). Alternatively, transfer in batches to a blender, then return to the pot.
08 - Stir in the grated cheddar cheese a handful at a time, stirring until fully melted and the soup is creamy.
09 - Taste and adjust seasoning as needed.
10 - Serve hot, garnished with extra cheddar and fresh herbs if desired.