To make the cookie dough using an electric mixer, break the almond paste into small pieces and place in a large bowl. Add egg whites. Beat with an electric mixer on low speed until smooth. Gradually add the sugar, beating until combined. Continue as directed.
Place cookies in layers separated by waxed paper in an airtight container; cover. Store at room temperature for up to 1 day, chill for up to 3 days, or freeze for up to 3 months.