Cut the peeled potatoes in half lengthwise, then cut each half into crosswise slices about 1/8 inch thick (do not use a food processor). Chop the onions into 1/4-inch pieces.
In a large skillet, heat 1 tablespoon of oil over medium-high heat. Add the potatoes and cook, stirring occasionally (covering the pan with a lid will make this go quicker). After about 5 minutes, add the onions and green pepper and continue to cook, stirring occasionally, until the potatoes and peppers are tender, about 5 more minutes. Season heavily with salt; potatoes require a lot of salt. Remove from heat.
In a large mixing bowl, lightly beat eggs. Add the potato-onion mixture and stir until well-mixed.
Add the remaining 1 tablespoon oil to a large skillet over medium heat and swirl to coat bottom of the pan. Add the egg-potato mixture and cook without stirring until the egg has set around the edges. Check, by lifting an edge, to see if the egg is beginning to brown on the bottom. When it starts to brown, place a large plate over the top of the pan, invert the pan and plate so that the omelet falls onto the plate, then slide the omelet back into the pan, browned side up.
Cook until the egg is completely set, about 1 or 2 more minutes. Cut into wedges to serve. This goes especially well with hot sauce.
Nutrition information per serving: