Grease two 8-inch cake pans with vegetable oil, and line with waxed paper. Grease waxed paper with vegetable oil. Set the cake pans aside.
Cream butter in a large mixing bowl; gradually add 1/2 cup sugar, beating well. Add 4 egg yolks, one at a time, beating well after each addition. Stir in milk and vanilla.
Sift together flour and baking powder. Sprinkle flour mixture over yolk mixture, 1/4 cup at a time; carefully fold in. Spoon batter evenly into prepared cake pans; set aside.
Beat 5 egg whites (at room temperature) until soft peaks form. Gradually add remaining sugar, 1 tablespoon at a time, beating until stiff peaks form and sugar dissolves. Spread meringue mixture evenly over batter in prepared cake pans, sealing to edges of pans. Sprinkle top of each with sliced almonds and cinnamon.
Bake at 350° for 30 minutes. Let cool 10 minutes in cake pans away from drafts.
Invert one baked meringue layer onto cooling rack; remove waxed paper. Immediately place on a serving platter, bottom side down. Spread top of layer with one-fourth of whipped cream. Invert remaining layer onto cooling rack; remove waxed paper. Place on top of whipped cream, bottom side down. Spread sides with remaining whipped cream. Chill thoroughly. Slice and serve on individual serving plates.