Place the potatoes in a medium saucepan and cover with cold water. Bring to a boil over high heat, then reduce the heat to low, cover, and simmer for 20–25 minutes, or until the potatoes are fork-tender.
Meanwhile, place the eggs in a separate saucepan and cover with water. Bring to a boil, then add a drop of vinegar, if desired, to help contain the egg whites if the shells crack. Cover the pot, reduce the heat, and simmer for 10–12 minutes for fully hard-boiled eggs. Remove the eggs with a slotted spoon and set aside to cool. Once cool enough to handle, peel and set aside.
When the potatoes are cooked, drain them and set aside until cool enough to handle. Peel the potatoes and transfer them to a bowl. Add the peeled hard-boiled eggs and mash everything together using a potato masher.
Add the salt, white pepper, and olive oil. Mix well with a wooden spoon until the ingredients are thoroughly combined and the mixture is smooth and fluffy.
Transfer the mashed potato and egg mixture to a serving plate and spread it evenly. Drizzle generously with extra virgin olive oil and garnish with sliced onions and fresh mint leaves. Serve warm or at room temperature with Arabic bread or pita bread.