Grease an eight-inch springform or round cake pan and line it with parchment paper. Press the parchment paper up on the sides of the pan to help hold the caramel.
For the pears, make a caramel by melting one-quarter cup of sugar in a small saucepan over low heat until golden brown. Add one-quarter cup of butter and stir gently until melted. Take the pan off the heat and stir in one tablespoon of dark rum and one tablespoon of ground ginger until the sauce is smooth. Leave the caramel to stand for twenty minutes, or until it cools enough to coat the back of a spoon.
Preheat the oven to 350°F.
Peel the pears and cut them into quarters. Remove the cores and cut each quarter into four long slices. Place the pear slices in the caramel and toss to coat. Arrange the pear slices in a fan shape in the bottom of the prepared cake tin.
To make the cake, add two large eggs, one-half cup of butter, and one-half cup of white sugar to a mixing bowl. Use an electric mixer and beat until smooth.
Mix in one cup of Bisquick, one teaspoon of ground ginger, and one-half teaspoon of ground allspice. Continue mixing until the batter is well combined.
Spoon the mixture over the pears and smooth the surface. Bake for forty minutes, or until the cake has well risen, and a toothpick comes out clean when inserted into the middle. Place a serving plate over the cake and carefully turn it over. Remove the base, sides of the pan, along with the parchment paper.
Slice and serve the cake warm with vanilla ice cream if desired.