Preheat oven to 375°. In a 10-in. cast-iron or other ovenproof skillet, melt butter over low heat. Add apple and 1/4 cup brown sugar. Cook and stir until crisp-tender, about 5 minutes. Stir in coffee; remove from heat., In a large bowl, beat oil, sugar, egg, egg white, vanilla and remaining 1/4 cup brown sugar until well blended. In another bowl, whisk flour, cinnamon, salt, baking soda and nutmeg; gradually beat into oil mixture. Gently spread over apple mixture., Bake until a toothpick inserted in center comes out clean, 18-22 minutes. Cool on a wire rack 10 minutes., Meanwhile, for drizzle, in a small saucepan, bring coffee and cream to a boil; cook until liquid is reduced to 1/4 cup, 10-12 minutes. Remove from heat; stir in confectioners' sugar. Let stand 10 minutes. Drizzle over cake.