Lost in the wilderness west of Jardim de Estrela is Melbourne Coffeehouse, a place that, outrageously, does not have its own website.
It serves the usual salmon/avocado/egg-based brunch suspects along with a couple of Portuguese touches. I had a flat white there and it didn't kick quite as hard as the ones from the Mill or Copenbrica; the eggs benny were tasty enough but they were served on a cheap, untoasted burger-type bun, which is a good way to save money and disappoint customers. I'll go back, but with my expectations tempered. It wants to be the Mill, but doesn't quite pull it off.
Bonus point: outdoor seating is nice, and the neighbourhood is quiet.
Bonus bonus points to whoever can suggest a better portmanteau than Copenbrica.