Cream butter and 1 cup sugar together. Beat in 3 eggs, one at a time. Mix in vanilla. Stir in flour, baking powder and salt gently. Add milk if needed.

Divide batter into 2 equal parts. Add food coloring to 1 part to make a deep pink color. Grease two 7-inch square pans. Spread batters into pans.

Bake at 350°F (175°C) until an inserted wooden pick comes out clean, about 25 to 30 minutes. Let stand in pans for 5 minutes. Turn out on racks to cool.

Trim edges from both cakes. Cut each cake lengthwise into 4 strips as wide as the cake is thick. Trim to make strips match. Heat jam slightly. Spread on sides to glue 2 pink and 2 white strips together checkerboard fashion. Spread all 4 sides of the completed cake with jam.

To Make Almond Paste: Mix almonds, confectioners' sugar, egg, lemon juice, and almond extract together. Knead until smooth, adding a bit of lemon juice or water if too dry to roll. Add only 1/2 teaspoon at a time. It will be stiff. Divide into 2 equal parts.

Roll 1/2 of the paste 1/8 inch or so thick on a surface lightly dusted with confectioners' sugar. Cut to fit the length of the cake, and long enough to cover 4 sides leaving ends uncovered. Lay cake on one end of the paste. Wrap to completely enclose all 4 sides of the cake pinching the paste to seal. Roll in granulated sugar.