Make the cake:
In a large bowl, cream butter and sugar with an electric mixer until smooth and creamy. Add eggs, one at a time and mix, after each addition, until well incorporated.
In a medium bowl, whisk together self-rising flour, cinnamon, nutmeg and ginger. Stir in pecans and raisins.
Gradually add flour mixture to wet ingredients. Beat until all the dry ingredients are well incorporated.
Stir in diced green tomatoes. Batter will be thick.
Pour into a well-seasoned 12 inch cast iron skillet. Spread evenly.
Bake in a 35o degree preheated oven for 60 minutes or until a toothpick inserted into the center of the cake comes out clean.
Remove from oven.
Make the icing:
Add chopped pecans to a hot skillet and toast for 5 minutes, stirring frequently, or until you can smell a toasted aroma and the pecans start to brown slightly. Remove from skillet and set aside. Wipe skillet clean and return to burner.
Reduce heat to medium. Add butter, stir occasionally until melted.
Gradually whisk powdered sugar into melted butter.
Whisk in a few drops of half and half until the icing is smooth and creamy.
While the cake is still hot, pour hot icing over top.
Sprinkle icing with toasted pecans.
Let cool for at least 30 minutes before slicing. Serve out of the skillet. Don't be ashamed.