Sauté onions and celery in bacon drippings over medium heat until tender (4-5 minutes).
Sprinkle flour, thyme, ground mustard, and black pepper over vegetables and stir to coat; cook and stir for 2-3 minutes.
Add Worcestershire sauce; cook and stir for 2-3 additional minutes.
Add bay leaf and white wine, cook and stir for 3-4 minutes while flour and seasonings thicken the wine and the alcohol evaporates.
Stir in chicken broth, carrots, potatoes and ham; simmer for 10-20 minutes or until vegetables are tender (time varies based on the size of the vegetable pieces).
Slowly stir in one cup of the milk, stirring constantly, until milk is thoroughly warmed. Repeat two more times with remaining milk (see note below).
Add shredded cheese, a little at a time, stirring to allow it to melt in the soup (see note below).
Finish with a small dash of nutmeg. Remove from heat.
Garnish with shredded cheese, green onions, potato skins (see note below), and bacon.