Beat butter and shortening in a large mixing bowl with an electric mixer on medium to high speed for 30 seconds. Add brown sugar, baking powder, baking soda, and salt; beat until combined, scraping sides of bowl occasionally. Beat in egg, milk, and almond extract until combined. Beat in as much flour as you can with the mixer. Stir in almond toffee pieces and any remaining flour with a wooden spoon.
Shape dough into two 10-inch-long rolls. Wrap in plastic wrap or waxed paper, chill in refrigerator for 4 to 24 hours or until firm enough to slice.
Cut rolls into 1/4-inch-thick slices. Place slices 2 inches apart on an ungreased cookie sheet. Bake in a 350 degree F oven about 9 minutes or until edges are firm. Transfer to wire racks and cool. Makes about 36.