What was the work of a cobbler?
Cobblers make shoes for people.
A cobbler is someone who makes shoes. They cut out the patterns from leather and sew them together, then nail them onto the hard shoe bottoms.
I haven't looked up the usage in the play, but a cobbler can have two meanings depending on how it is used. In one use a cobbler is a person who makes shoes ( I suspect that this is the usage in the play since in the time frame that is what is used for a "shoemaker"). A cobbler can also be a baked pie of fruit.