To make the pie crusts, add the flour, butter, salt, and sugar to the bowl of a food process and pulse until there are no large chunks of butter left (small pieces are fine)
Slowly add in the ice water, and continue to pulse until the dough comes together into a single clump. Remove from the food processor, divide in half, and refrigerate until ready to use. (You'll only need 1/2 of the dough for this recipe, so I like to wrap the second one tightly in plastic wrap and freeze it to use later. It freezes perfectly!)
Preheat oven to 375F. Roll out your tart dough into a circle about 1/4 inch thick, and fit it into your 10-inch tart pan with removable bottom. Set the crust in the refrigerator while you make the filling.
In the bowl of a stand mixer with the paddle attachment (or with electric beaters), cream together the butter and sugar until light and fluffy. Add the salt, egg, and almond extract and mix well to combine.
Finally add the almond flour and the all purpose flour and mix until combined.
Spread the almond mixture evenly into the bottom of your pie shell. It helps to dollop the filling evenly across the surface of the pie crust before spreading it out.
Add the sliced pears on top of the almond filling, arranging them any way you like. I took groups of 6-9 thin slices, fanned them out slightly, and pressed them gently into the filling.
Bake for about 35 minutes. The filling should be puffed up and golden brown. I tented mine with a piece of aluminum foil for the last 10 minutes of baking to keep it from getting too brown on top.
Remove from the oven and allow to cool before dusting with powdered sugar.
*I sliced the 'cheeks' from my pears and then laid them cut side down and thinly sliced. Do not peel the pears!