In a large skillet, cook potatoes and onion in butter until tender and lightly browned. Meanwhile, in a large bowl, beat eggs, milk, Italian seasoning, salt and pepper.
Pour over potato mixture. Sprinkle with pepperoni. Cover and cook on medium-low heat until eggs are set, 10-12 minutes. Remove from the heat. Sprinkle with cheese; cover and let stand for 2 minutes. Cut into wedges.