In a large skillet, combine the water, sugar, cinnamon, and lemon juice. Bring to a boil, then reduce to a simmer. Add the pears and cook for about 30 minutes, until tender. Let cool, then slice each pear thinly, keeping the top intact so the slices fan out but remain connected.
In a bowl, mix the ground almonds, butter, sugar, and eggs until smooth. Stir in the flour and vanilla extract. Transfer to a piping bag.
Cut the puff pastry into 12 squares. Cut slits into 6 of the squares to create a lattice pattern. On the remaining squares, pipe a layer of almond cream and place a poached pear on top.
Cover each tart with a latticed square, pressing the edges to seal. Trim any excess pastry. Brush with the beaten egg.
Preheat the oven to 400°F (200°C). Arrange the tarts on a lined baking sheet and bake for 20–25 minutes, until golden brown and crisp.
Dust with powdered sugar, let cool slightly, and serve warm.