Bring the oats and 4 cups water to a boil in a saucepan over medium-high heat. Reduce the heat to a simmer and cook, stirring frequently, until very thick, 3 to 4 minutes. Remove from the heat and cover to keep warm.
Meanwhile, heat a wok or large skillet over medium heat until smoking and add the peanut oil. Working in batches if necessary, crack the eggs into the wok and cook to desired doneness.
Transfer the oats to 4 shallow bowls and top each with a fried egg. Sprinkle the scallion greens over each bowl and pass the chili sauce, peanuts and soy sauce at the table for garnishing. Top with the additional traditional Taiwanese accompaniments, if using.