Place an 8 or 10 inch cast iron skillet over a burner set to medium.
To the skillet, add the first amount of butter and allow it to melt.
Add the first amount of sugar and ginger to the butter in the skillet and stir to mix, until the sugar mostly melts into the butter.
Raise the heat slightly and arrange the pear quarters evenly in the butter mixture, and allow to simmer in the pan, while you prepare the cake batter. You want them to get a bit of color on the bottom sides and begin to get soft. They will give off some juice and that is fine - just let them keep cooking.
Cream together the butter and sugar, until light and fluffy.
Beat in the eggs, and then the vanilla.
Whisk the dry ingredients together in another bowl.
Add the flour mixture to the butter/egg mixture in 3 parts, beginning and ending with the dry ingredients and alternating with the buttermilk.
Remove the skillet from the heat, and spoon the batter over the pears as evenly as possible. It may seem like it won’t be enough, but it will puff up and cover the fruit as it bakes.
Bake at 400º for about 30 minutes, until a toothpick inserted just into the cake comes out clean - the top will be nicely browned and the edges should be bubbly.
Cool about 10 minutes in the pan, and then, using care, invert the cake onto a large plate. The pan will be very hot still.
Cut in wedges and serve warm with whipped cream. Refrigerate leftovers.
Notes
If you don't have an iron skillet, you can still make this cake. Just make the pear topping in a regular skillet, and transfer it to a well buttered 8 x 8 inch pan before you cover it with the cake batter. It will take slightly longer to bake this way - 40 minutes or a bit more.