Trim the stems off the broccoli heads and chop into small florets.

In a large pot over medium heat, combine the butter and onion and sauté until translucent. Add the flour and stir until the mixture lightly browns. Stir in the milk and mix until the contents reach a simmer. Turn the heat to low and add the stock. Simmer for 5-10 minutes.

Mix in the broccoli, carrots, salt, pepper, and nutmeg. Simmer for 10-15 minutes. Add the cheese and stir until it melts and combines with the other ingredients.

Enjoy!