Melt butter in a large pot over medium heat. Add onion and carrots, and cook until soft, about 3-4 minutes.

Add flour and stir to combine.

Slowly pour in broth, then milk, then cream. Add nutmeg. Season with salt and pepper to taste.

Stir in 2 cups of chopped broccoli. Cover and reduce the heat to low and let simmer for 30 minutes until the broccoli is tender.

Remove from heat and use an immersion blender to purée. You can leave this part out if you like a chunkier soup. Then add in 2 cups of shredded cheddar cheese and mix in until fully melted. The addition of cheddar cheese makes the soup a bit thicker and gives it a cheesy flavour, so it is a crucial step. Serve immediately in individual bowls and garnish with extra cheddar cheese if desired.