Heat a pan over medium-low heat. Add 4 oz butter, let it melt and start to foam. Stir frequently until the butter becomes golden in color and some brown bits start to collect at the bottom. Be careful not to burn the butter. Set aside to cool to room temperature.
In a medium bowl, whisk or sift together flour, cream of tartar, baking soda, and salt.
In a large bowl or the bowl of your mixer, cream the softened butter and the cooled browned butter with the sugar at medium-high speed thoroughly until light and fluffy.
Add the eggs one at a time, and mix thoroughly.
Reduce mixer speed to low, and slowly add the flour mixture. Mix until just combined.
Using a spatula, stir in the toffee bits.
Place dough in the refrigerator until just cool enough to handle and roll into balls, about 30 minutes.
Preheat oven to 400°F.
Combine cinnamon and sugar in a small bowl.
Using a small scoop or about 1 tablespoon of dough, form balls, and roll each ball in the cinnamon sugar mixture to coat all sides.
Place dough balls about two inches apart on a cookie sheet.
Just before baking, take your three middle fingers and press the balls down slightly, until they are about a half inch thick.
Bake for 8-10 minutes, or until barely set and slightly golden. They will puff up at first while baking, then flatten out.
Cool for a few minutes on the pan, then remove and cool completely on cooling racks.