Melt butter in medium sized pot and add shallots or onions and salt. Sauté until onions are translucent.
Add garlic and let cook for 30 seconds then add pepper, mustard and turmeric and stir well.
Add flour, and with a whisk, combine everything well and let cook for 1 to 2 minutes.
Slowly add 2 cups of broth, stirring well so no lumps form, and then continue with the half and half or other type of milk that you prefer.
Once the liquids are smoothly incorporated let simmer on low heat for 10 minutes, if you think it is too thick then go ahead and add some or all of the third cup of broth and incorporate well and bring back to a simmer then add broccoli and carrot.
Let cook for another 10 to 15 minutes (until broccoli is tender), stirring every few minutes.
Add most of the cheese (leaving about 1/2 cup for garnish) and stir until melted, about 5 minutes then turn off heat.
Ladle into a bowl and garnish with some shredded cheese, chopped bacon, and green onions or chives.
Serve with your favorite sandwich and enjoy!