In a large bowl, cream together the butter, shortening and vanilla. Blend in confectioners' sugar, one cup at a time, beating well after each addition. Beat in the milk and continue mixing until light and fluffy. Add cinnamon. Keep icing covered until ready to decorate.

Heat the oven to 400 degrees F.

Lightly coat an 8-inch cake pan with butter and dust with all-purpose flour.

Sift the cake flour, baking powder, and salt into a large mixing bowl. Beat in the butter one teaspoonful at a time, using an electric mixer set on low speed, until the mixture resembles coarse sand. Beat in the sugar a tablespoon at a time, until the mixture resembles fine damp sand. Beat in the eggs one at a time. Add the vanilla and milk, and beat on medium-high, just until blended. Do not overbeat.

Pour into the prepared pan and bake until a wooden skewer inserted in the center comes out clean — 30 to 35 minutes.

Cool cake in the pan on a wire rack for five minutes. Un-mold and cool completely before icing and adding cranberry filling.