For the record, this kind of construction is also done in some closer relatives to English, like Norwegian ("brødet mitt") and Icelandic ("brauðið mitt"). I believe I've seen similar examples of this in 19th century German too ("das Brot meines"), although "mein Brot" is certainly how it's done now.
Greek isn't necessarily trying to be difficult here. ;)
How about Italian "il mio pane" with both definite article and possessive adjective, just like here?
Oh, I'm sure there are lots of examples out there; I just went with the languages I'm personally familiar with!
And for that matter, English can even employ a similar contruction--"the bread of mine." While English pretty strictly requires "of," it's not necessarily done that way in other languages (thus, "brødet mitt," not "brødet (av) mitt").