Notes: Four English muffins, split and toasted, can be used instead of the toast.
In an 11- to 12-inch frying pan over medium-high heat, stir onions and butter often until onions are limp and lightly browned, about 10 minutes.
Meanwhile, shell eggs and chop.
Mix a little broth with flour to make a smooth paste, then add to remaining broth and mix into onion mixture. Add milk and stir over high heat until boiling, then stir about 2 minutes more.
Add eggs to sauce and mix well.
Spoon sauce onto toast. Sprinkle with parsley and add salt to taste.
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