Except
expression
除く is "to exclude." This is the te-form, and it means "except." So, something like "please get everything except broccoli," because who wants broccoli?
のぞいて
The reading comes from 除く. It's just the te-form of it.
彼女は厄介な仕事をうまくやってのけた…あることを除いて、だが。
She managed to do well on those tricky jobs... except for that.