Surprisingly, there's a simple recovery strategy that works pretty well. Drain the eggs in a colander and let them stand for a minute or two. Put a pan with some oil over high heat (don't use butter because of butter's low smoke point). When the oil is hot, flash fry the scrambled eggs and ensure they never get to sit in one place long enough to burn. Return to a plate as soon as the eggs are nicely piping hot again.