Put a soup pot over medium-high heat and melt the butter in the bottom. Add the celery and onion and sauté until the veggies are tender. Should take about 5 to 7 minutes.

Add the chicken broth, potatoes, and vinegar to the pot. Cover it up and bring it to a boil. Reduce heat to low and simmer until the potatoes are tender, around 20 to 25 minutes.

In a small bowl, combine flour, salt, pepper, and milk, and whisk it all together until it's nice and smooth. Stir the flour mixture you just made into the soup pot and cook it until the soup is heated through and thickened. You'll want to keep a constant stir going while you wait for it. Finally, add the cheese and give one more good stir until it's melted. Ladle it into a bowl and warm up!