Dice the potatoes into evenly sized and fairly small (although not super tiny) dice. You want them small enough so they more or less fit in a single layer in an 8-inch nonstick skillet and will cook quickly. Aim for about 1/2-inch dice—no larger.
Place the potatoes in the skillet and add the water, oil, and salt and crank the heat to medium-high. Cover and bring to a boil. Reduce the heat slightly, cover, and set a timer for 5 minutes. Let the potatoes cook, stirring once or twice if you think of it, while you prep the rest of your ingredients. By the end of the 5 minutes, the water should have just evaporated, and the potatoes should be barely tender and maybe even have started to brown a little.
Uncover the potatoes and use a spatula to loosen them from the skillet. Cover again and cook over medium to medium-high heat, stirring occasionally, until lightly browned, 2 to 5 minutes. If using dried herbs/spices, sprinkle them over the potatoes now. In a small bowl, lightly beat the eggs.
Pour the eggs over the browned potatoes, strew with the scallion, and scramble until the eggs are just set, maybe a minute or so.
Sprinkle the eggs and potatoes with the cheese and fresh herbs, remove the skillet from the heat, and let the whole shebang rest for a few minutes until the residual heat melts the cheese and finishes cooking the eggs. (If you're in a hurry and don't mind losing a little crispness on the potatoes, you can cover the skillet so the cheese melts more quickly and evenly.)
Scoop the mess of fried potatoes and eggs from the skillet and onto plates. Pass the forks.