Bring a small saucepan of water to a boil, then carefully lower the 2 whole eggs into the water and simmer for 7 minutes for a jammy yolk.
While the eggs boil, whisk the 2 egg whites in a small non-stick skillet over medium-low heat until just set and fluffy, then remove from heat.
Transfer the boiled eggs to an ice bath for 3 minutes to stop the cooking process, then gently peel and slice them in half.
In a large mixing bowl, whisk together the extra virgin olive oil, lemon juice, sea salt, and black pepper until emulsified.
Add the arugula, thinly sliced red onion, and capers to the bowl and toss thoroughly until the greens are evenly coated with the dressing.
Arrange the dressed arugula on a plate and top with the scrambled egg whites, the halved soft-boiled eggs, and the ribbons of smoked salmon.