Remove the fillets from oil and set the oil aside. Finely chop the anchovies and mix with the parsley and garlic. If the mixture is a bit stiff, add back in some of the anchovy oil until the mixture is spreadable. Set to the side. Preheat your broiler.
Spread each slice of bread with butter and toast under the broiler until it is a light golden brown.
While bread is toasting, scramble the eggs in a double boiler with the cream. When they are thickened, but still a tad bit underdone, remove from the heat and season with salt and pepper.
Divide the eggs between each slice of toast and top with cheddar. Return to the boiler until cheese is melted and starting to brown. Enjoy immediately.