Step 1: In a large saucepan over medium heat melt 1/4 stick of butter. While whisking add in flour and continue whisking until a roux is formed.
Step 2: Slowly whisk in the half and half until the roux has dissolved and then whisk in chicken broth. Allow to simmer for 15 minutes, stirring occasionally.
Step 3: While that liquid is simmering melt one teaspoon of butter in a small pan. Add the onions and carrots and saute 2-3 minutes or until onions start to soften. Remove from heat and set aside.
Step 4: Add onion and carrot mixture along with the broccoli to the liquid. Cover with a lid and simmer on low heat for 15 minutes, stirring occasionally.
Step 5: Remove the soup from the heat and use either an immersion blender or a blender to puree the soup ingredients until smooth. Return soup to pan and stir in nutmeg and cheese until melted. Serve immediately.
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