Toss the pears and other ingredients together gently (the pears will break easily, so be careful)
Set aside for 15 minutes
Mix the two flours, salt and sugar in a bowl and then, using a pastry cutter or two forks, cut in the almond butter and shortening until they are evenly dispersed through the flour. The shortening should be in little pieces, about the size of peas.
Using a fork to mix the flour, drizzle in the ice cold water, a tablespoon at a time, until the dough comes together in a ball.
Place the dough in plastic wrap, shape into a disk, wrap tightly, and place in the refrigerator for three hours or overnight. You can even make this a few days ahead and freeze it, then thaw it ovenight in the refrigerator. Remember to keep the dough cold at all times.
Assemble the tart:
Take the refrigerated dough and, on a floured surface, roll it into a disc about 12 inches in diameter (most tart pans are 10 inches in diameter, and you want to give another inch or so to cover the sides. When rolling any pie dough keep rotating the dough and flouring the surface and rolling pin to ensure it is not sticking to the surface.
Fold the disc in half, then lift it into the tart pan. Open it to cover the tart pan. Very gently, with your fingers, push the dough into the corners so that the dough fits evenly into the tart pan. Use a rolling pin to roll over the edges of the tart pan and cut off the excess dough.
Refrigerate the tart pan with the dough inside for 10 minutes.
Working quickly, arrange the pear slices in the pan in concentric circles, overlapping them. You can try any design you like, or even go free-form, but this simple design I made is an easy one and doesn't take any time at all. If you have broken pear pieces, put them at the bottom and use the good ones on top.
Pour any juice at the bottom of the bowl into the tart pan.
Place on a baking sheet and bake 55-60 minutes in a preheated 375-degree oven. The filling will be mostly set but might appear slightly jiggly in parts, which is okay.
Cool thoroughly on a rack before serving, which gives the filling time to thicken and solidify.