If you only had your Brazilian passport, it would bring up some subtle questions about obligations when crossing the border, your rights as EU citizen, what you may or may not do with an expired passport, what the consequences might be in practice, etc. but in that case you don’t have to worry about all that. A national ID card is enough, plain and simple.
You can use it to go through the exit border check, to enter the Schengen area, to establish your right to live in the EU and to satisfy German ID obligations (Ausweispflicht). I have done all this multiple times with mine and German and EU law actually state as much explicitly. As long as you can prove you are an Italian citizen, there can be no concern about any overstay or lack of stamps in your other passport. There is also no obligation to carry or hold an EU passport for EU citizens (as opposed to holding an official ID document in general, which can be mandatory in some countries and useful to establish your citizenship).
And your Brazilian passport will take care of entering Brazil and satisfying airline checks. In some rare cases (another user experienced that in Sweden), it seems border guards also want to see that you will be able to enter your destination before letting you exit the Schengen area but the Brazilian passport ought to take care of that as well (and I don’t think German border guards care at all).
Credit:stackoverflow.com‘