Preheat oven to 300 F.
In a large bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add brown sugar, baking powder, and salt. Beat until combined, scraping down sides of bowl occasionally.
Beat in egg and vanilla until combined. Beat in as much flour as you can with mixer. Using a wooden spoon, stir in any remaining flour.
Stir in toffee pieces.
Shape dough into 1 1/4-inch balls. Place 2 inches apart on an ungreased cookie sheet.
Dip the bottom of a glass in granulated sugar and flatten each ball to about 1/4-inch thickness. Bake about 20 minutes or until edges are firm but not brown. Transfer cookies to a wire rack; cool.
Adapted from Better Homes and Gardens Christmas Baking 2009