Fill a medium saucepan two-thirds full with water and bring it to a boil over medium heat.
While the water heats, set a colander in the sink, line a rimmed baking sheet or large plate with two paper towels, and have a large slotted spoon ready.
Crack all 4 eggs into a bowl and whisk them for about 20 seconds until blended.
When the water is boiling, add two generous pinches of kosher salt (the water should taste like the sea).
Stir the water in a clockwise motion to create a whirlpool, then pour the whisked eggs into the center, cover the pot, and wait 20 seconds.
Uncover and remove the eggs with the slotted spoon, holding them in the pot while you pour the cooking water through the colander to drain.
Gently slide the eggs into the colander, shake them side to side to remove excess water, then transfer to the paper towel–lined baking sheet.
Bring up the paper towels around the eggs to form a pouch and gently press to remove remaining water, then transfer the eggs to a serving plate.
To serve, drizzle the eggs with extra-virgin olive oil and a few splashes of chile oil, then top with chopped parsley, fleur de sel, and freshly ground black pepper.
