Preheat you smoker to 425 degrees.
Toss the potatoes oil, thyme, salt, and pepper together in a large bowl and spread out on a sheet tray.
Place the tray in the smoker and cook for 45 minutes.
While the potatoes are cooking, place the tablespoon of butter in a large pot and melt; add the onions and carrots and cook until onions are translucent.
Add the ham, stock, and milk and bring to a boil.
Reduce to a simmer and add the cheese, stir well.
While the cheese melts, melt the quarter cup butter in a sauce pan and add the flour; stir until incorporated to form a roux.
Add the roux to the soup mixture and stir until thickened.
Remove the potatoes from the smoker and add to the soup, stirring well.
Taste, adjust the seasonings, and serve!