Preheat the oven to 400° F, and line a baking sheet with parchment paper.
Roll the puff pastry out on a floured counter to make it about 1-inch wider in all directions.
Use a pizza cutter to cut out 8 equal-sized rectangle pieces of dough.
Move each dough rectangle to the baking sheet. Use a fork to prick holes all over the dough, avoiding the edges and leaving a 1/4-inch border so that the edges of the pastry will puff up.
In a small food processor, blitz the flour, 1 tablespoon of sugar, almonds, and salt. Add the almond extract and lemon juice once the mixture is powdery, and blend again.
Peel and thinly slice each pear into 5 slices per quarter of a pear.
Place 2 teaspoons of the almond mixture on the dough rectangles, spreading it out but avoiding the edges by 1/4-inch. Repeat with all of the dough rectangles.
Lay 5 slices of pear (which is 1/4 of a pear) onto each dough rectangle. Sprinkle the remaining tablespoon of sugar on top of the sliced pears.
Finally, beat the egg with a generous splash of water, and use a pastry brush to spread it on the edges of all of the tarts.
Bake the tarts for 16-17 minutes. Let them cool for 10 minutes before serving.
Notes:
To make this for two, use only 2 pieces of dough and half a pear, and reserve the remaining almond mixture in the freezer for another day. The bake time is the same for 2 tarts.