Place the milk in a small saucepan and bring to a simmer over low heat. Heat the butter in a medium saucepan over medium heat. Add the onion and cook until soft. Stir in the flour and cook for 1 minute. Slowly whisk in the warm milk, and continue whisking until thickened. Season with salt and cayenne pepper. Continue cooking for 5 minutes, whisking occasionally. Remove from the heat and stir in the cheese. If the sauce is too thick, thin it with a little extra milk. Serve sauce warm with potato chips for dipping.
Place the potato slices on a baking sheet between layers of paper towels to make sure they are very dry before frying. Heat oil in a large, heavy saucepan until the temperature of the oil reaches 400 degrees F on a deep-fat thermometer. Fry the potatoes in small batches until golden brown on both sides, turning once. Remove with a slotted spoon and place on a brown paper bag or another baking sheet lined with paper towels to drain. Season with salt immediately. Serve hot with the blue cheese dipping sauce.