How to stuff bread puffs (Gougeres)
Gougeres are not stuffed, at least in Bourgogne. The dough contain the cheese (Gruyere) and nothing is added to it after the fact. Well cooked gougeres have the cheese in the center still moist and gooey, giving the impression of an after the fact filling when in reality the cheese has been in the dough all along. If the inside of your gougere is dry, it's been in the oven for too long. Note that using anything else than gruyere, or eventually comté, is probably not going to get the gooey delicious result.

I guess the only way to add a filling would be to do it the same way you do profiteroles: simply slice the gougere horizontally with a sharp knife, add whatever you want inside, and put the top back in place.