While the onions are cooking, peel the potatoes and cut them into 1/2-inch cubes or half-moon-shaped slices. In a saucepan of boiling salted water, cook the potatoes until almost tender, about 8 minutes. Drain in a colander and allow them to cool there. When the potatoes have cooled, combine the onions and potatoes. The onion and potato mixture may be made 1 day ahead and chilled, covered.
In a large bowl, whisk together the eggs, scallions, Italian seasoning spice blend, remaining 1/2 teaspoon salt and the pepper. (I add a lot of black pepper to this omelet, but start with a little and see what you prefer.) Add the cooked onion and potato mixture and stir to combine.
In the same nonstick skillet used to sauté the onions, heat the remaining 3 tablespoons of oil over medium-high heat until hot but not smoking. Add the egg mixture, spreading the potatoes evenly across the pan. Reduce the heat to medium and gently stir eggs for about 1 minute or until the omelet begins to set. Shift the skillet so that 1/4 of the omelet is directly over the center of the burner and cook for 1 minute. Shift skillet 3 more times, cooking each skillet quarter for 1 minute. Reduce the heat to low, center the skillet over the burner and continue to cook the omelet until almost set, about 4 minutes.
Slide the omelet, bottom side down, onto a baking sheet or a large heatproof platter. Then invert the omelet back into skillet. Cook the other side of the omelet over low heat until golden, about 4 minutes. Slide the omelet onto a platter and allow to cool before serving. Garnish with chopped scallion if you like.
If made ahead and refrigerated, allow the omelet to come to room temperature before serving. This may be served warm or at room temperature.