Wash potatoes and prick them. Heat butter on medium high in a heavy fry pan (butter will turn brown). Add potatoes and cook covered while tossing occasionally. When potatoes begin to soften (about 35 minutes), turn down heat and add shallots. Cook for about 10 minutes, then add basil and cook for about 2 minutes while tossing. Salt and pepper to taste. Garnish with chopped basil.