Gently beat eggs with a big pinch of salt and some pepper in a medium bowl with a fork. Heat oil in a medium non-stick or cast iron skillet over medium heat until shimmering. Add eggs and cook, stirring constantly with a rubber spatula, until barely set and still slightly runny (eggs will continue to cook after removing from pan), about 1 minute. Immediately transfer to a serving dish. Sprinkle with pine nuts, sumac, and parsley. Drizzle with olive oil and serve immediately with flatbread.