Cut butter into tablespoon-sized pieces and place in a skillet over medium heat. Stir continuously as the butter melts, until it turns a golden-brown color and begins to smell nutty. This usually takes 8-10 minutes depending. Watch the butter carefully so that it doesn't burn.Remove from heat and pour into a large freezer-safe container and place it into the freezer for 10 minutes. Stir the butter, then freeze for an additional 10 minutes, or until it cools completely and has turned solid.
In a large bowl, cream the sugar and butter together for 2 minutes, until light and fluffy.
Add the milk, eggs, and vanilla, and beat for an additional 1-2 minutes.
In a separate bowl, stir together the flour, cream of tartar, baking soda, and salt.
Pour the dry ingredients into the butter mixture and mix on low speed until the flour is incorporated and no longer visible.
Add the toffee bits to the bowl and mix on low speed or by hand, until they are distributed throughout the batter.
Refrigerate dough for at least 2 hours.
When ready to cook, preheat your oven to 375 degrees F.
Mix ¼ cup of sugar with 1 tablespoon of ground cinnamon.
Scoop dough into quarter cup portions (see the notes for directions on making smaller cookies). Roll each portion into a ball, then place in the cinnamon-sugar mixture and coat the top and sides of the dough ball, leaving the bottom without any added sugar.
Place on a baking sheet with 3 inches of space between each ball of dough. Bake for 9-11 minutes, or until the edges of the cookie are just beginning to turn brown.
Remove from the oven and cool for several minutes on the baking sheet, then transfer a cooling rack and cool completely.
When cooling the brown butter you can also place it in the refrigerator for 2 hours.
If you do not have cream of tartar, increase the baking soda to ¾ teaspoons and also add 2 teaspoons of baking powder.
This recipe is for large, bakery-style cookies. For smaller cookies, use a 2 tablespoon scoop to portion. Place the cookies 2-inches apart on a baking sheet and cook at 375 degrees F for 8-10 minutes. Yield: 32 cookies
To give the cookies more of a bakery-style appearance, place some individual toffee bits on the top and sides of each ball of cookie dough prior to baking.