Melt butter in a large soup pot.
Add onions and sweat for 1 minute.
Whisk in flour to make a roux.
Add chicken broth.
Add nutmeg, mustard powder, garlic powder, salt, and pepper.
Bring to medium-high heat.
Add cheese, 1/4 cup at a time whisking continually until the cheese is melted and smooth.
Add broccoli and carrots.
Slowly whisk in half n half.
Cook on medium-low for 10 minutes whisking frequently.
Turn heat to a low simmer and cook for 20 minutes.
Garnish and serve immediately.