Heat a large pot to medium heat and saute the onion in ½ tbsp. melted butter until translucent, about 5 minutes. Remove from pot and set aside. In the same large pot whisk together the remaining 1½ tbsp melted butter and flour over medium heat for 3 to 4 minutes. This will create a roux, which is the base of your soup.
Slowly whisk in half and half and the chicken stock. Add salt and pepper to your liking here. Let it simmer for about 20 minutes. Stirring occasionally.
Add the broccoli, carrots, and onions. Stir to cover the veggies with the stock. Let them simmer on medium-low for about 25 minutes until the broccoli and carrots are tender. Stirring occasionally. Add more salt and pepper here to your liking.
Add nutmeg, more salt and pepper, and sharp cheddar cheese. Stir to combine and cook until the cheese has melted then serve!
Can store in the fridge for up to 5 days in an airtight container. You can also freeze this soup! Dump the soup into freezer bags and store it in the freezer for up to 3 months. How can my kids help? They can help add in the seasonings. Tips: If soup is too clumpy at the end, add more chicken stock until it's at the consistency you desire.