Heat 18 charcoal briquettes.
Sift together flour, baking powder, and salt.
Using an electric mixer, cream together butter, Neufchatel cheese, 1/2 cup sugar, and vanilla. Add eggs, one at a time. Blend in flour mixture.
Mix together apples, allspice, and 1/4 cup sugar. Fold into the cake batter. Pour batter into greased Dutch Oven.
Place 12 briquettes on the lid of the Dutch Oven and 6 on the bottom. Bake for 1 hour, rotating the briquettes.
Combine powdered sugar and milk. Drizzle on cooled cake.