Place 2 pounds of peeled and cut potatoes in a medium pot and cover with 4 cups chicken or vegetable broth. Bring to a boil. Reduce heat, cover, and simmer until potatoes are tender, about 15-20 minutes.
Transfer potatoes and broth to the blender (you may have to work in batches). Cover the top of the blender with a kitchen towel and blend on low to puree the potatoes. Set aside.
In a large soup pot, heat 3 tablespoons of olive oil over medium heat. Add 1 small onion, chopped, and cook for about 5-8 minutes until soft and translucent. Add garlic and cook for another minute until garlic is lightly browned. Be careful not to burn the garlic.
Add pureed potatoes, a can of evaporated milk, 2 tablespoons of Worcestershire sauce, 1 teaspoon salt, 1 teaspoon ground mustard, 1/2 teaspoon black pepper, and additional 4 cups of broth to the pot. Bring to a boil.
When soup is boiling, reduce heat and add the beer. Let cook for five minutes.
Reduce heat to low and stir in cheese until melted.
Serve with croutons, crumbled bacon, minced chives, parsley, black pepper or additional cheese.