Preheat the oven to 350°F (175°C) and line baking sheets with parchment paper.
In a large bowl, cream together the softened butter and both sugars until light and fluffy, about 2–3 minutes.
Beat in the egg, egg yolk, and vanilla extract until smooth.
In a separate bowl, whisk together the flour, baking soda, cream of tartar, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Fold in the toffee bits.
Scoop the dough into 1.5 tablespoon-sized balls (or use a cookie scoop). Roll the dough balls in extra sugar if desired.
Place the balls 2 inches apart on the prepared baking sheet. Slightly flatten the tops with your fingers or the bottom of a glass.
Bake for 9–11 minutes, until the edges are set but the centers remain soft. The cookies will crinkle as they cool.
Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
