Melt the butter in a large pot over medium-low heat. After it has melted, gradually add the flour while whisking continuously to create a thick paste. Continuous whisking for less than 30 seconds should do this. You do not wish to set it on fire. Simply stir until well incorporated and a thick paste forms. Before beginning the recipe, make sure the flour is measured out and ready to use. The milk should also be measured and prepared for pouring.
After adding the full milk, mix everything together. Simmer for approximately five minutes, whisking often, until it thickens.
Bring the soup pot to a simmer, or a gentle boil around the rims, after adding the veggie broth.
* If necessary, increase the heat to medium to bring the broth and soup to a simmer, or a gentle boil. Keep a close eye on it and whisk often to prevent the milk from scorching.
Add the black pepper, kosher salt, mashed potatoes, and shredded cheddar cheese. Stir to melt the cheese and mix everything together.
When the soup has thickened and the cheese has completely melted, it is ready to serve. Serve with sliced green onions, sour cream, more shredded cheese, and chopped smoked turkey.