Trim the stems off of the broccoli heads, then chop into small florets.
2. Step
Melt the butter in a large pot over medium heat. Add the onion and sauté until translucent, about 5 minutes. Add the flour and stir until the mixture lightly browns, 2–3 minutes. Pour in the half-and-half and cook, stirring constantly, until simmering. Reduce the heat to low and add the vegetable stock. Bring to a simmer and cook for 5–10 minutes, until thickened.
3. Step
Mix in the broccoli, carrots, salt, pepper, and nutmeg. Simmer for 10–15 minutes, until the vegetables are tender. Add the cheese and stir until it melts and combines with the other ingredients.
