A few more ideas as I think about it. These are mainly ethnic bakeries, not really what you're looking for, but they are authentic at what they do.
First, the place most likely to be of interest to you is in Burbank, and I'm blanking on the name, but I'll post it next week. They have probably the best cannoli in the LA area, and a small, delicious frosted cake that they call a "tea cake." I'll get back with the name.
Second, it's not European, but I quite like some of the stuff that can be had at El Gallo Giro (multiple locations; the one I go to is off Roscoe in North Hollywood). I've mentioned this one before; the attraction is that, as Mexican bakeries go, this has about the freshest, moistest stuff you'll find.
Again, on the non-Euro front, Guatalameca, on Beverly, is a Guatamalan bakery listed in Counter Intelligence. I wasn't blown away by it (though some of the small cakes were fine), but I really liked the Guatamalan tamales being sold outside by a few ladies. (They are nothing like a Mexican tamale).
The restaurant Rincon Chilleno, a Chilean place on Melrose has a little bakeshop right beside it. The pastries are quite excellent, and all are filled with various types of caramel. Quite interesting.
Goldilock's is a filipino bakery of all things. They have a sponge roll filled with custard that I found quite good. It's around Vermont and 2nd.
The muffins at Ammo - a little breakfast place on Highland - are the best I've ever had.
Again, I am blanking on the precise name / location, but there are a few interesting Armenian bakeries in the Little Armenia section of Santa Monica Blvd not far from Normandie. There is one on the south side of Santa Monica, and another a few blocks east on the north side. Both sell the same things - Bourek (sp?), a delicious pastry pouch filled with flavored cheese or spinach (not at all similar to the greek version, made with phyllo), and a few types of savory Armenian type pizza. Limited selection, but quite good.
Those are the things that come to mind in the domain of baked goods.