Heat a skillet over medium heat. Add the olive oil, the green parts of the spring onion, and canned mushrooms. And cook over medium heat for a few minutes, stirring constantly.
Once they start to soften add the cream cheese, and season with salt and pepper.
Cook for a minute or two, until the cream cheese melts.
On a lightly floured surface roll each piece of dough into a 8 inch (20cm) circle.
Place each onto a parchment paper lined baking sheet.
Spread cheese over each dough leaving about ½ inch (2cm) around the edge.
Spread mushroom & cream cheese mixture on top of cheese.
Fold dough over the filling. And brush with beaten egg.
Bake for about 20 minutes until slightly golden.
Remove from oven and make a well into the center of each galette.
Crack 4 eggs into 4 small different bowls. If eggs are too large remove some of the whites. Add an egg on each galette and bake for 10 minutes more until eggs are cooked.