Thaw the puff pastry sheets (if using frozen) but make sure they are still cold.
Pre-heat the oven to 190C / 370F (no fan).
Cut the pears lenghtwise, remove the cores, and then cut the pears into very thin slices. Soak any excess juice with the help of paper kitchen towels.
Unfold one of the puff pastry sheets and cut it into 6 rectangles, as in the process image.
Place half a tablespoon of almond flour in the middle of the pastry, then place one-half pear onto each. Sprinkle the pears with brown sugar.
Whisk the egg with a splash of milk and apply egg wash all around the pastry (not the pears).
Continue with the other puff pastry sheet until you get 12 tarts. Bake 6 at once.
If at any point the puff pastry becomes warm to handle, pop it into the freezer or fridge for a few minutes to chill. Do not force the pastry if it is too warm.
Bake the tarts at 190C / 370F (no fan) for about 45 minutes. Cover them after about 15 minutes to avoid them browning too much.
Let them slightly cool in the baking tray for 3 minutes then move them onto a cooling rack.
The pear tarts are the best served fresh. Any leftovers can be stored at room temperature for 2-3 days in an air-tight container.
Notes
Removing any excess juice out of the pears is key to avoiding a soggy bottom on your pear puff pastry tarts. We are applying two tactics here: 1. Once the half pears are cut into very thin slices, place them onto a kitchen paper towel that will soak in some of the excess moist 2. Use almond flour under the pears while baking the pastry.
Work as quickly with the pastry as you can as over time, when the pastry warms, it will stick and would make it very difficult to handle.
Check the bottom of the pastry to see whether it is well baked.