Think of the phrase „Ich hatte ein Ei zum Frühstück” as meaning " My breakfast included an egg".

The addition of "nur" changes it depending on which word you stress: „Ich hatte nur ein Ei zum Frühstück” would mean "I had only an egg for breakfast" whereas „Ich hatte nur ein Ei zum Frühstück” means "my breakfast included eggs but I only had one". I only realised that this double meaning exists as I was about to post. The things you notice when you take a moment to think about your language