Slice the pears as thinly as you can (you don’t need to peel them).
In a saucepan over medium heat, melt the butter. Stir in the brown sugar until it’s dissolved. Add the sliced pears and cook, stirring frequently, until they’re softened after about 10 minutes. Remove from the heat and set aside to cool.
Preheat the oven to 375°F. Line a baking sheet with parchment paper.
Roll out the two sheets of the thawed, cold puff pastry on a lightly floured surface until the folds are sealed together. Each should be roughly 30 cm x 25 cm.
Use a large circular cookie cutter or the rim of a large drinking glass to cut out circles from the dough.
Place about one tablespoon of blue cheese in the center of a dough circle. Then use a slotted spoon to remove a large spoonful of cooked pear slices from the pan, allowing any excess liquid to drip off, then place it on the pastry, leaving a ½-inch space around the edge. Repeat with the remaining pastry circles.
Fold the outer ½-inch edges of the dough in towards the center to create mini galettes, so the filling doesn’t leak out (see photos in the blog post above for reference).
Arrange them on the prepared baking sheet, spread out by at least 2 inches.
Whisk the egg in a small bowl with one tablespoon of water, then brush it onto the top of the dough of each pastry. Sprinkle the chopped nuts evenly over each pastry.
Bake for 15 to 17 minutes until the puff pastry is puffed up and golden. Cool for a few minutes, then enjoy.