Preheat broiler. Cook potato in salted boiling water until tender, about 10 minutes. Drain. In a bowl, beat together eggs, milk, basil, salt and pepper until eggs are just blended. In a 10 inch (25 cm) ovenproof skillet, heat oil over medium heat. Add onion, peppers and garlic. Saute 2 minutes. Add potato and saute 2 minutes longer. Pour eggs over vegetables in skillet. Cook over low to medium heat until eggs are almost set but still moist on the surface, about 10 to 12 minutes. Occasionally lift edges to allow uncooked egg to run to bottom of skillet. Sprinkle top with cheese. Place under broiler until cheese melts, 2 to 3 minutes. Cut into wedges to serve.
Preparation: 10 minutes
Cooking: 20 minutes