In a large bowl, combine the flour, sugar, baking powder, baking soda, salt, cinnamon, ginger, and allspice. Use a fork or a wire whisk to thoroughly combine the dry ingredients.
Next, chop the butter into small pieces. Add the butter to the bowl that contains the dry ingredients.
Using a pastry blender or a fork, cut the butter into the flour mixture. Continue mixing until the mixture resembles cornmeal with tiny blobs of butter evenly distributed throughout the mixture.
Put a doubled-over paper towel on a small plate. Place the pear halves on the paper towel and fold the paper towel around the pear halves to blot as much syrup from the pears as you can. Then unwind the paper towel from the pears and then use a paring knife to dice the pear halves into small bits.
Using a spatula, put the pears in the dry mixture and stir to combine them into the mixture.
Measure the buttermilk in a glass measuring cup and add the vanilla to it, stirring it to combine. Stir the dough just until the scone dough begins to stick together and all of the dry ingredients are moistened. You might not need all of the buttermilk mixtures or you may need a little extra if the dough is too dry. You do not want the mixture to be wet and sticky. Just take your time and add a little buttermilk at a time. However, you don’t want to overmix the dough either, because that will lead to tough scones.
Once the dough is just right, turn it out onto a lightly floured surface. Press the dough into a 7 or 8-inch circle with your hands and cut it into eight equal wedges.
Line a large baking sheet with parchment paper and place the scones on the baking sheet about two inches between each wedge. Put the baking sheet in the refrigerator for about half an hour.
When the time is almost up, preheat the oven to 400 degrees. Brush the tops of the scones with one tablespoon of heavy cream.
Adjust the oven rack so that it is in the center of the oven, and bake the scones for 15 to 20 minutes, or until they are lightly browned on top.
As the scones are baking, whisk the powdered sugar, the remainder of the cream, and the cinnamon together in a small bowl. Set this glaze aside until it is time to remove the scones from the oven.
Transfer the scones to a plate or a wire rack to cool. When the scones are mostly cool, after about 20 minutes or so, you can drizzle them with the glaze.