In large bowl, beat butter with an electric mixer on medium-high speed for 30 seconds. Add brown sugar, baking powder and salt. Beat until combined. Beat in egg and vanilla until combined. Beat in as much of the flour as you can with mixer and then combine the rest with a spoon. Stir in toffee pieces.
Shape dough into 1 1/4 inch balls. Roll in granulated sugar.
Place 2 inches apart on ungreased cookie sheet and flatten slightly with bottom of a glass.
Bake about 20 minutes or until edges are firm, but not brown.