Heat butter until melted in a sauce pan over medium heat. Stir in flour and cook 1 minute. Slowly whisk in milk, continuously stirring until flour/butter is incorporated fully into the milk. Turn heat down to medium-low and continue to cook until the milk is creamy and thickened- about 8 minutes
Add cheese wedges into the hot sauce and whisk until the cheese is melted and incorporated. Stir in salt, pepper, turkey, and ham, bring to a simmer to heat up the meat and then remove from the heat.
Season additionally with tobasco sauce, if desired, and top hot baked potatoes with the sauce.