Saute minced onions in butter on medium heat for about two minutes, until brown and crisp.
Add the mushrooms and olive oil. Sauté on medium, stirring occasionally, for about 10 minutes until lightly browned and mostly dry. Remove from the heat and allow to cool.
Place your puff pastry on a baking sheet that is lined with parchment paper. Lightly flour the parchment, unfold dough and roll gently only as needed to straighten and make even.
Using the tip of a knife, gently score a 1 inch square border on the pastry sheet without cutting all the way through.
Using a fork, pierce the dough inside the square frame (not the border), in multiple spots. Using a pastry brush, brush entire top of pastry with egg to add a nice sheen to your crust and to create a moisture barrier for your other ingredients.
Bake the tart for 15 minutes in the center of the oven. Remove from oven and use fork to gently flatten down any puffed areas.
Spread sautéed mushrooms and crumbled Canterbury soft goat cheese evenly across the sheet, sprinkle with thyme leaves and add a light dusting of nutmeg and bake for an additional 10 minutes.