Preheat oven to 400 degrees.
Roast walnuts on a sheet pan in the oven for 8 minutes or until just toasted.
Allow them to cool.
Once the walnuts are cool, process them in a food processor with the brown sugar until they resemble sand. About 20-30 seconds.
Roll out the thawed puff pastry sheet to 9"x12" rectangle. No need to measure, just make it larger than a sheet of computer paper. Place the puff pastry on a sheet of parchment in a sheet pan.
Mix the egg yolk with 1 tsp water. Brush the egg wash onto the puff pastry.
Sprinkle the walnut mixture on top of the puff pastry leaving a 1/2" border around the edge.
Place the pears on top of the walnuts. I start with the middle diagonal line and work out from there. Start at the top and just barely overlap the pear slices as you work towards the bottom.
Place the pear and puff pastry in the 400 degree oven and bake for 30 minutes.
Sprinkle the blue cheese evenly over the puff pastry and bake an additional 5 minutes or until melted.
Pull out of the oven and allow to cool for 5 minutes. Serve warm or at room temperature.