Preheat the oven to 400 degrees F (200 degrees C).

Make cookies: Beat sugar, butter, shortening, eggs, and vanilla in a large bowl until smooth and creamy.

Whisk flour, cream of tartar, baking soda, and salt together in a separate bowl. Gradually mix dry ingredients mixture into the wet ingredients just until combined.

Stir in Toffee bits

Shape dough into walnut-sized balls.

Make cinnamon-sugar: Combine sugar and cinnamon in a small bowl or zip-top plastic bag.

Place dough balls in cinnamon-sugar and roll or shake until coated. Place 2 inches apart on ungreased baking sheets.

Bake in the preheated oven until set but not too hard and edges are lightly golden, about 8 to 10 minutes, switching racks halfway through.

Remove from the oven and transfer to wire racks to cool.