Chop your potatoes, green onions, and jalapeños. Set aside green onions and jalapeños. Place chopped potatoes in a bowl of water to soak while you prepare other items.
Chop ham, careful to slice around the bone. Chop about 1 pound into pieces for your soup. Slice remaining ham to use for sandwiches or snacks!
Add 5 cups of milk to a pot and warm over medium heat for about 5-8 minutes, make sure it doesn't burn.
While milk is warming, add butter to a large stock pot and melt. Then, add flour to melted butter, constantly whisking to combine to create a roux.
Carefully pour 4 cups of warm milk into roux, whisking to combine. Be sure to scrape anything off the bottom so nothing burns. Cook for about two minutes, until it thickens. Add additional cup of milk, til desired thickness.
Add chopped potato, half of the sliced green onions, and ham to the stock pot. Stir to combine. Bring to a boil, then simmer for about 15-20 minutes.
Check your potato doneness and continue cooking til desired texture. Then, turn off heat and add shredded cheese, stirring to combine.
Ladle into a bread bowl and top with more cheese, green onions, chopped jalapenos, and maybe sour cream!