In a large pot, sauté the onion in 1 tablespoon melted butter until onions are soft. Add in the flour and 1/4 cup melted butter.
Stir with the onions over medium heat for about 3-4 minutes until the onions are soft.
Slowly whisk in the half and half and chicken stock.
Add the broccoli and carrots. Simmer, covered on medium-low for about 25 minutes until the broccoli and carrots are tender.
Add nutmeg, salt, pepper and sharp cheddar cheese. Let the cheese melt and then serve.
Enjoy!
Notes
For a smoother soup, you can puree this soup with an immersion blender or regular blender. Refrigerate the leftovers in an air tight container for up to 4-5 days.I used fresh chopped broccoli for this recipe but you can use a bag of frozen broccoli instead.