Prepare the crust:
Preheat the oven to 375°F. Line a sheet pan with parchment.
Divide the puff pastry in half and roll each piece into a 10-inch round approximately ? inch thick. Refrigerate for 20 minutes.
Prepare the filling:
Place the almond paste in a food processor and pulse until the paste is broken apart. Add the butter, flour and egg, and process until smooth.
Assemble the pithivier:
Place the first round of dough on the prepared sheet pan. Brush the edge of the dough with the egg wash and mound the frangipane on top, leaving a 1-inch border all around. Fan the pear slices on top of the frangipane.
Place the second round over the first and press down on the edges so that they adhere. Using a sharp knife, cut the edges of the pastry to create a fluted edge. Pierce the center of the pastry to create a steam hole and then, using the same sharp knife, score the pastry, starting at the steam hole and gently etching a curved line to the edge of the pastry. Repeat this curve evenly around the pastry.
Bake for 20 to 25 minutes, until the pastry has puffed and is a deep golden brown.
Adapted from Pie It Forward