Cream butter and powdered sugar. Add egg and vanilla, and mix well. Mix in flour and baking soda to make smooth dough. Stir in pecans and candied cherries until evenly incorporated.
Chill dough for 1 hour, then divide into 4 portions. Roll each piece into a log about 7 inches long and 1 ½ inches around. Roll in wax paper and chill for at least 3 hours.
Preheat oven to 350 degrees.
Unwrap rolls and slice about ⅛-inch thick. Bake on parchment-lined cookie sheet for 13 to 15 minutes or until lightly browned.