Melt butter in large saucepan. Add onion and garlic and sauté until tender. Stir in mustard, cayenne and turmeric.
Add flour and stir until completely combined. Add broth slowly, a half cup to a cup at a time, whisking to keep flour lumps from forming. When incorporated bring back to a boil and stir until thickened.
Add carrots and broccoli and simmer until tender, about 15 minutes.
Stir in half and half, then add cheese in handfuls, stirring to melt. Taste and adjust salt.
I am not a health professional and nutrition data is calculated programatically. Accuracy may vary with product selection, calculator accuracy, etc. Consult a professional for the best information.