Slide your hand under her!, I have a broody RIR with eggs and I can't get my hand near her- she pecks hard!
my mom used to take the feed scoop and put it over the evil broody hen's head when she needed to check the eggs.. they couldn't peck her then and she could quickly check the eggs.. it was a lot less stress for both of them
I just reach under.. I've been pecked but I don't let it bother me