Boil or steam potatoes until they are slightly undercooked in center. Let cool. Peel the skin with a small knife.
Slice potatoes across about 1/2" thick. Set aside.
In a large bowl whisk the eggs together with water and about 1/2 cup chopped parsley with some salt and pepper.
Dredge the potato slices in flour. Add the potatoes to this mix and set aside.
In a nonstick pan over medium-high heat add some of the olive oil and add potatoes slices two at a time, making sure they are coated well with the egg. Pan fry until golden brown on both sides, adding more oil if necessary. While potatoes are cooking melt 2 tablespoons butter in a large pot and cook the garlic and onion until translucent.
Add the mussels, wine and remaining parsley then cover and cook until mussels are wide open.
Remove mussels from the pot. Set aside. Bring the wine mixture to a boil and add butter. Whisk it in until it is melted. Salt and pepper to taste.
To Serve: Place mussels in bowl. Pour the wine liquid over them and sprinkle with remaining parsley and top with the Idaho slices.