Clean the fresh pioppini, cutting a thin slice off the bottom of each stem, rinse in cool water to remove any dirt, then pat dry with paper towels. Heat the oil in a large skillet and sauté the chopped onion for a few minutes. Add the pioppini mushrooms, season with salt and pepper, and cook for 10 minutes on low heat.
In the meantime, in a large pan melt the butter over medium-low heat. Add the gnocchi and sauté for 5 minutes.
To prepare the fried eggs, heat a large skillet with a little olive oil over medium heat. Break the eggs into the skillet, paying attention not to break the yolk. Cook for a minute, season with salt and pepper, cover with a lid and continue cooking over low heat for 4 minutes (or until done as desidered).
Transfer the fried eggs to a plate, add gnocchi, mushrooms and a few parsley leaves, then serve.