1. Heat oven to 400°F.
2. Beat butter, shortening and 1 cup sugar in large bowl until fluffy. Add eggs; beat thoroughly. Stir together flour, cream of tartar, baking soda and salt; gradually add to butter mixture, beating until well blended. Stir in toffee bits.
3. Stir together remaining 1/3 cup sugar and cinnamon. Shape dough into 1-1/4-inch balls; roll in sugar-cinnamon mixture. Place on ungreased cookie sheet.
4. Bake 9 to 11 minutes or until lightly browned around edges. Cool slightly; remove from cookie sheet to wire rack. Cool completely. Makes about 5 dozen cookies.