Step 1In a medium saucepan, combine the sugar, brown sugar, butter and cream and heat to a boil while stirring constantly. Stir in the rum or vanilla and remove from heat.
Step 1Heat the oven to 350 degrees. Use 1 tablespoon butter to grease a 9-by-13-inch pan.
Step 2Combine the remaining butter with the sugar in the bowl of an electric mixer and cream until light, about 2 minutes. Add the eggs one at a time and blend, scraping the sides of the bowl.
Step 3Stir together the flour, baking soda, salt and spices and beat on low speed, half at a time, into the butter mixture, mixing well. Stir in the apples and pecans, mixing well so that all the ingredients are well dispersed. Scrape into the prepared pan and spread evenly.
Step 4Bake 45 minutes, or until a toothpick inserted into the center comes out clean. Cool on a rack while making the sauce.
Step 5Cut the cake and spoon the sauce over.