In a big mixing bowl, mix the all-purpose flour, powdered sugar, salt and softened butter, using the tip of your fingers, until the butter is fully incorporated and you have a mixture that resembles sand.
Add the egg yolk. Mix with your hands until you have a uniform dough. Gather the dough in a ball, wrap it, and place it in the fridge for 1 hour.
Take the ball out of the fridge. Using a rolling pin, roll it out to fit your tart pan.
For the filling
Preheat oven to 350 degrees Fahrenheit.
Mix the softened butter, the granulated sugar, the almond flour, and the egg until you have a uniform paste.
Use a fork to make little holes on the tart crust (pictured). Cut the pear halves in slices and place them on the crust as though the pear halves were not sliced (see picture). (Please note: we are using the pears without the syrup from the can).
Pour the almond paste around the pears as pictured.
Sprinkle with sliced almonds. Bake in oven for 25 minutes. Enjoy warm or cold!