I've only tried broccoli twice - once I don't think she actually ate any - it was all over the floor! The second time we were out at the pub and I gave her some to munch on. She had a good chew on it but I don't think it made things any worse!
LJ's tried toast with butter, carrots, slightly roasted sweet potato (so it doesn't fall apart when she picks it up), banana, rice cakes, broccoli, mashed potato, peas. More recently grapes and cucumber (she was definitely upset before these) and today she's tried pear and a tiny bit of apple for the first time.
I think it's probably just solid food in general.