It should be “I broke fast”, not “I breakfasted”, there’s already a verb in there but people have forgotten, TBH “To have break fast” is quite questionable grammar. It’s different in German, “Frühstück” means “early piece”, an adjective-noun compound which then can be fed through the usual verbification rules.
English does that all the time, breakfast is actually a very good example. Toothpaste. Hairstyle. Bedroom.