In a saucepan, combine the eggs with water to cover by 2 in. (5 cm.) and bring to a boil over high heat. Lower the heat to medium-high and cook for 6 minutes. Drain and place under cool running water to cool. Peel the eggs.
Using the large holes of a box grater, and working over a large bowl, grate the eggs. Add the mint, green onions, and red pepper flakes and mix well. In a small bowl, whisk together the olive oil and lemon juice to taste, then drizzle over the egg mixture and toss to coat lightly and evenly. Season with salt. Serve at room temperature or slightly chilled.