Stump puffballs are edible and best when gathered young as they have a firm texture, exquisite smell but mild taste, and not as good as field puffballs. But they are very prolific and make a good meal if cooked carefully.
Before you pick them, cut one open to check its maturity. When young, they have a firm white flesh but if they are old, the area near the top will have turned yellowish and they will become spongey. This is from the formation of powdery spores which are eventually puffed out through an opening in the top. Once a puffball has reached this stage it loses all taste and texture. Best sautéed and added to a dish. See below.
Cut each puffball in half and discard any old ones. Sauté gently in good quality olive oil. Once they start to soften, turn the heat right down and add a good slosh of sherry, lots of salt and pepper and a splash of soy sauce. Leave to sweat on a very low heat. Beat three eggs together with a splash of milk. More salt and pepper and pour them over the puffballs. Quickly grate Parmesan cheese over the pan and then stir in as the eggs start to set. Delicious!