The word 'rumbled' for a dish of a mashed-up food is known at least since the memoirs of C Shaw of 1837, where he tells: "My appetite was excited at seeing a sturdy monk making what was in Scotland a favourite dish with boys, I mean a pot of rumbled potatoes." Rumbled eggs are known at least since the 1850 'Spirit of Times' (1 June) "It's something between rumbled eggs and omelette, and is a compound fit for the gods." (OED). The dish seems have to been popularised in the USA during the mid 19th Century.
Original Receipt from 'Godey’s Lady’s Book' magazine, Philadelphia, USA, c1860.Ingredients:
3 eggs
2 oz. butter
1 tsp. cream or milk
Buttered toast
Beat up three eggs with two ounces of fresh butter, or well-washed salt butter; add a teaspoonful of cream or new milk. Put all in a saucepan and keep stirring it over the fire for nearly five minutes, until it rises up like a soufflé, when it should be immediately dished on buttered toast.