Cook potato in salted boiling water until tender, about 10 minutes.
Beat together eggs, milk, basil, salt and pepper until eggs are just blended.
In a 10-inch (25cm) ovenproof skillet over medium heat, heat oil.
Add onion, peppers or zucchini, and garlic.
Sauté 3 minutes.
Add potato and sauté 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, lifting the edges to allow uncooked egg to run to bottom of skillet.
Sprinkle top with cheese.
Place under broiler until the cheese melts, 2 to 3 minutes.
Cut into wedges to serve.