Preheat oven to 350 degrees F. Line a large baking sheet with a Silpat baking mat or parchment paper and set aside.
In a medium bowl whisk together flour, baking soda, cornstarch, salt, and cinnamon. Set aside.
Place butter and brown sugar in the bowl of an electric stand mixer. Beat on medium speed until light and fluffy, about 3 minutes. Turn off the mixer and scrape down the sides of the bowl with a spatula. Add the egg and vanilla extract, and beat on medium speed until combined.
With the mixer on low, slowly add the dry ingredients. Mix until the just combined. Stir in the toffee bits.
Using a spoon or cookie scoop, form tablespoons size balls of cookie dough. Roll balls in brown sugar. Place on balls on prepared baking sheet, about 2 inches apart. Bake cookies for 10 to 12 minutes, or until lightly browned around the edges. Do not over bake. Cool on the pan for 2 minutes. Transfer cookies to a wire cooling rack and cool completely. Store in an air-tight container for up to 4 days.