Before you begin, wash the puffball (if needed), then peel it. Slice it into ⅛" slices, then chop one slice into 2" to 3" pieces. Add more or less based on your preference and the size of your mushroom.
Melt butter in a nonstick skillet and sauté mushroom pieces until golden on both sides. Add chopped chorizo and sauté for 1 minute longer.
Whisk eggs in a bowl, then arrange mushrooms and chorizo on half of the pan before pouring whisked eggs over them. Tilt the pan to distribute the eggs.
Arrange olives and cheese over the mushrooms and chorizo. When the eggs begin to set, fold one half over to cover the ingredients.
Continue to cook over low heat until the egg is cooked through and the cheese is melted. Serve with fresh salsa or your favorite hot sauce.
Notes
Since the chorizo was pretty salty and spicy, I did not add additional seasoning. If you substitute bacon, you may want to season with a pinch of salt and black pepper.
An even easier way to make this dish is to scramble it instead of making an omelette. Zero skill required!
If you have more giant puffball mushrooms than you can eat while fresh, sauté first, then freeze it in portions. Freezing it raw can leave the mushroom with an unpleasant texture and foul-smelling liquid once thawed.
Another option is to dehydrate it for longer storage. Once dried, it takes up less space and can be rehydrated for soups, sauces, and other dishes.
Sautéed puffball is delicious in pasta, risotto, soups, stir-fries, pizza, or simply served as a side dish. Because its flavor is relatively mild, there are plenty of puffball mushroom recipes you can make with this versatile mushroom.
If you've harvested more than you can reasonably use, give some to friends or family who enjoy cooking with wild mushrooms. A giant puffball can go a surprisingly long way.