Butter and flour lightly an 8" x 8" baking dish.
In the large bowl of your mixer, using the paddle attachment, beat the butter just until it's softened, on medium-low speed.
Into this add the brown sugar, and beat until fluffy. Add in the eggs one at a time, beating well after each, then add in the molasses and the ginger root.
In a separate bowl, whisk together the flour, baking soda, salt, allspice, cloves, and nutmeg. Add this, alternately with the buttermilk, into the mixing bowl on low speed. Beat just until combined.
Gently fold the thinly-sliced pear into the batter. Spread the batter into the prepared pan and bake at 350 for about 35 minutes, or until a toothpick inserted into the middle comes out clean. Cool the cake in its pan on a cooling rack.
With a peeler, remove the zest from half of the lemon. In a medium size heavy-bottomed saucepan, combine the zest, 2 Tbsp of juice from the lemon, 1 cup of water, and the 1/4 cup sugar. Heat over a medium-low flame until the sugar dissolves, stirring periodically.
Peel, core, and quarter the four pears. Add them into the sugar mixture. Cook this uncovered until the pears become tender, perhaps 10 minutes or more. With a slotted spoon, remove the pears from the pan and put them in the bowl of a food processor.
Continue cooking the liquid in the saucepan until it has reduced by half, then remove and throw away the lemon peel. Pour the liquid into the food processor bowl.
Pulse the mixture until it is completely smooth. Put it in a small bowl, and stir in the cognac. Serve the sauce warm, draped over individual pieces of cake. Sprinkle confectioner's sugar on the pieces first, if you like.