Step 1Defrost the puff pastry according to the package directions.
Step 2Place the almonds in a food processor. Process until finely ground.
Step 3In the bowl of an electric mixer, cream the butter and sugar until light and fluffy. Beat in 1 egg and the brandy, almond extract and ground almonds. Beat in the flour.
Step 4Scrape this frangipane mixture into a bowl, cover tightly and refrigerate until firm, at least 30 minutes or up to several days.
Step 5Peel the pears and cut in half lengthwise. Remove the core and stem. Cut the pears into one-fourth-inch lengthwise slices. Sprinkle with the lemon juice and cover with plastic wrap to prevent browning.
Step 6Roll out 1 sheet of puff pastry on a lightly floured work surface into an 11-inch square about one-eighth-inch thick. With a very sharp knife, trim off 1 inch around the edges. Cut straight down; if you drag the knife, the layers will compress and will not puff as high. Cut the square into 4 equal squares, turn the pastry over and set aside. Roll out the second sheet and follow the same procedure. Save the pastry scraps for another use.
Step 7Line 2 baking sheets with parchment paper. Make an egg wash by beating the remaining egg and the cream together.
Step 8Picturing a square folded on the diagonal into two triangles, spread 1 1/2 tablespoons frangipane onto half of the pastry, leaving a half-inch border. Place 4 to 6 slices of pear on top, rounded side facing the corner. Cut the fruit to fit if necessary.
Step 9Carefully brush the egg wash on the pastry border so it does not drip over the edge. Fold over to form a triangle. Gently press down the sides to seal. Place the turnover on the parchment paper and repeat to form 7 more turnovers. Reserve the remaining egg wash.
Step 10Refrigerate until the pastry feels cold and firm, about 15 to 20 minutes. Heat the oven to 400 degrees.
Step 11Brush each turnover with egg wash, making sure not to let it drizzle over the edges. (Egg wash on the edges will inhibit the dough from rising.) Sprinkle each with crystal sugar.
Step 12Bake for 15 minutes. Reduce the heat to 350 degrees and bake until puffed and golden brown, about 15 to 20 minutes. Serve warm or at room temperature. Pastries are best eaten the day they are baked.