Heat oven to 375°F.
Combine flour, baking powder and salt in medium-size bowl. Beat together on medium-high speed butter, sugar, egg and vanilla in large bowl until light and fluffy, about 2 minutes. On low speed, gradually beat in flour mixture until combined. Stir in toffee bits.
Roll 2 teaspoons dough into a ball and place on ungreased baking sheet. With flat-bottomed glass with bottom dipped in flour, press dough to form 2-inch circle. Repeat with remaining dough, spacing cookies 1 inch apart.
Bake in 375°F oven 7 to 10 minutes or until golden and set. Let cool on baking sheet on rack 1 minute. Transfer cookies to rack to cool.
Melt chocolate and shortening in small saucepan over low heat, stirring. Sandwich together 2 flat sides of cookies, using about 2 teaspoons chocolate each. Drizzle outsides, if desired. Store airtight at room temperature up to 1 week.