Preheat oven to 425 degrees.
Wash asparagus under cool water. Pat dry with paper towels. Trim ends from stalk.
Place asparagus stalks in a bowl, drizzle with olive oil and sprinkle with half of salt and pepper.
On a clean work surface sprinkle flour. Lay out puff pastry sheet working on 1 sheet at a time.
Use a rolling pin to roll pastry dough into a thinner square about twice its size.
Line two baking sheets with parchment paper and spread each pastry square on separate sheets.
Use a sharp knife to cut each pastry sheet into squares 6 squares for a total of 12.
Mix together soften goat cheese, Gruyere, thyme leaves and remaining salt and pepper .
Lay 3 stalks of asparagus diagonally across each pastry square. Spread a small spoonful of cheese mixture on stalks.
In a small bowl beat egg for egg wash.
Use a pastry brush to brush each corner of the pastry dough. Careful wrap the asparagus by pulling pastry over and pressing it together. Crimp well with fingers and use egg wash to help seal edges.
Bake in oven for 12-15 minutes or until asparagus is tender and the pastry has puffed up and become golden brown.