Preheat a gas grill to medium-high, leave one burner off.
Sift together the flour, baking powder, baking soda, salt, ginger, cinnamon, nutmeg, mace, and allspice into a medium-sized bowl. Set aside.
Grate 1 of the pears. In a small bowl, combine the grated pear, egg yolks, molasses, and honey. Stir until blended. Add 1/4 cup hot water and stir until honey and molasses are evenly blended. Stir wet ingredients into dry ingredients.
In a large bowl, whip egg whites until stiff peaks form. Fold egg whites into batter.
Melt butter in a 10-inch cast-iron skillet on the grill over direct heat. Add brown sugar and cook until it darkens slightly, about 5 minutes. Remove from heat. Thinly slice the remaining pear. Arrange pear slices in the skillet in a spiral shape.
Pour batter over the pears in the skillet and place the pan on the grill over indirect heat. Close the lid and bake until the cake springs back when lightly touched, about 20 minutes.
Let cake cool for 10 minutes and then turn out onto a cake plate. Garnish with the walnuts and serve.