1. Heat oven to 350°F. Lightly grease cookie sheet or line with parchment paper.
2. Stir together flour, baking soda and salt; set aside. Beat butter, granulated sugar, brown sugar and vanilla in large bowl until well blended. Add eggs; beat well. Gradually add flour mixture, beating until well blended. Stir in toffee bits. Drop by rounded teaspoons onto prepared cookie sheet.
3. Bake 9 to 11 minutes or until lightly browned. Cool slightly; remove from cookie sheet to wire rack. Cool completely.
4. Line tray with wax paper. Place chocolate pieces and shortening in medium microwave-safe bowl. Microwave at MEDIUM (50%) 1 minute; stir. If necessary, microwave at MEDIUM an additional 15 seconds at a time, stirring after each heating, until chocolates are melted and mixture is smooth when stirred.
5. Dip about one-half of each cookie into melted chocolate. Shake gently and scrape cookie bottom on edge of bowl to remove excess chocolate. Place on prepared tray. Refrigerate until chocolate is firm, about 30 minutes. Store in cool, dry place with wax paper between layers of cookies. Makes about 48 cookies.