In a large bowl, whisk together eggs and milk. Add the next 6 ingredients and mix well. Let mixture stand 5 minutes. Preheat broiler. Heat oil in a large oven-safe skillet over medium heat. Add egg mixture and cook 3-5 minutes, until almost cooked through to the surface, frequently smoothing the top with the back of a large spoon. Place skillet under broiler; cook 1-2 minutes, until top is done. Sprinkle with shredded cheese and return skillet to broiler. Broil 1-2 minutes, until cheese is golden. Slice into 4 equal wedges and serve warm or at room temperature.