In a medium saucepan, combine the potatoes and enough cold water to cover; bring to a boil, then lower the heat and simmer until just fork-tender, 15 to 20 minutes. Drain, then chop into small cubes. Using the same saucepan, add the potatoes, 2 teaspoons olive oil, 1/2 teaspoon salt and 1/4 teaspoon pepper and cook over medium-high heat until golden-brown, about 10 minutes. Stir in the peas and yogurt. Cover and keep warm.
Meanwhile, in a small bowl, beat 1 whole egg, 1 egg white, 2 teaspoons water and a pinch each of salt and pepper for 1 minute.
In a small nonstick skillet, heat 1 teaspoon olive oil over medium-high heat. Pour in the eggs and cook, stirring, until partially scrambled, about 1 minute. Lower the heat and tilt the pan to spread the egg evenly. Spoon one-quarter of the potato mixture over half of the eggs and cook until the bottom is set, about 1 minute. Fold over the other egg half to enclose the filling and cook until warmed through, about 30 seconds. Slide the omelet onto a plate and serve. Repeat Steps 2 and 3 with the remaining ingredients to make 3 more individual omelets.