Grease an 8x8x2-inch baking pan; set aside. For crust, beat the 1/3 cup butter in a medium mixing bowl with an electric mixer on medium to high speed for 30 seconds. Add the 1/4 cup granulated sugar and beat until combined. Beat in 1 cup of the flour (mixture will be crumbly). Press the mixture into the prepared pan. Bake in a 350 degree F oven for 10 minutes.
Meanwhile, combine remaining all-purpose flour and the 2 tablespoons granulated sugar in a small mixing bowl. Cut in the almond paste and the 2 tablespoons butter with a pastry blender until crumbly. Set almond paste mixture aside.
Spread jam over top of the hot baked crust. Sprinkle almond paste mixture over the jam. Sprinkle with sliced almonds. Bake in the 350 degree F oven for 20 to 25 minutes or until topping is golden. Cool in the pan on a wire rack.
For icing, stir together powdered sugar and 1 teaspoon milk. Add additional milk, 1/4 teaspoon at a time, until icing is easy to drizzle. Drizzle over cookies. Cut into squares. Makes 16 squares.