Preheat oven to 400 degree F. Line a baking sheet with parchment paper or silpat.
In a medium bowl, add the chives and thyme leaves into the goat cheese, stir until the herbs are well distributed. Season with salt and pepper to taste. Set aside.
Wash, pat dry and trim off the tough parts of the asparagus ends. Cut into thirds. Set aside.
On a lightly floured work surface, unfold the puff pastry and gently roll it with a rolling pin to seal the seams. With a pizza cutter, divide dough into 4 equal size squares.
With a pairing knife, gently create an 1/2-inch border on all 4 portioned dough. Be careful not to cut through the puff pastry. With a fork, gently prick on the puff pastries within the border. Evenly divided the goat cheese mixture onto the puff pastries and spread the mixture with the border into a thin layer.
Place the asparagus onto the goat cheese mixture in a single layer. Place the puff pastry onto the lined baking sheet. With a pastry brush, brush egg wash onto the border and bake for 15 to 18 minutes, or until the edges are golden brown. Cool the tarts slightly. Serve warm.