To begin, dice the onion, shred the carrots (if not already shredded), and grate the cheddar cheese and set off to the side.
Warm up a larger pot over medium heat on the stove. Add the butter and onions and sautee until soft. Sprinkle the flour over the mixture. Cook and stir over medium heat for 2 minutes.
Add half & half and chicken broth & whisk together.
Stir in the broccoli and shredded carrots and let it sit for 25 minutes on low heat or until the broccoli and carrots are nice & tender.
Add your salt & pepper to taste., along with the cheese and stir until melted. Add in nutmeg if desired and you're ready to serve!