Mix scallions, rice, edamame, and vinegar in a small bowl; season with salt and pepper.
Heat oil in a nonstick skillet over medium-high heat. Crack eggs into skillet; season with salt and pepper and cook until whites are set around the edges, about 1 minute. Flip eggs and cook to desired doneness, about 30 seconds for a runny yolk.
Divide rice among bowls; top with eggs, avocado, and hot sauce and basil.