Line a 9" springform pan with parchment, and grease and flour the pan. Beat the egg whites with one-third of the sugar and, in a separate bowl, beat the egg yolks with another third. Soften the butter and cut into small pieces, them mix this with the remaining sugar and beat until light and creamy. Place the three mixtures into one large bowl, add the flour and vanilla extract and blend thoroughly. Transfer two-thirds of the mixture to another bowl and to this add the cinnamon, nutmeg, and allspice powder and stir to blend well. Pour one-third of the spiced mixture into the pan and bake at 350°F for about 10 to 12 minutes, until firm, then add half the plain mixture and bake until this is also firm. Repeat the process three more times; spiced, plain, and ending with spiced. Turn out onto a wire rack and allow to cool before serving.