In a large, microwave-safe bowl, melt butter in 15-20 second bursts in the microwave. This is the bowl you'll make your cookie dough in, so give yourself plenty of extra room. Stop when there are a few solid pieces of butter left — stir gently until they melt. Set aside to cool 25-30 minutes (you should see some butter starting to solidify around the very edges).
While butter cools, combine flour, salt, cream of tartar, and baking soda in a bowl. In a separate bowl mix together sugar, cinnamon, and cayenne for topping and set aside.
Whisk both sugars into cooled butter until it begins to thicken and is very smooth and pale in color, about 1-2 minutes (seriously, set a timer!). Add egg yolks one at a time, whisking for at least 30 seconds after each. Add the vanilla and whisk vigorously 60 seconds more.
Add the flour mixture all at once. Switch to a spatula and stir gently but firmly. At first it will seem like there is too much flour, but keep stirring and folding the mixture over itself and it will combine. When there is still a bit of flour in the bottom of the bowl, add the chocolate chips and continue stirring until you have a cohesive dough.
Use a 2 tablespoon scoop to portion the dough onto a quarter sheet pan lined with parchment paper. Then roll each dough ball in your hands to smooth it out into a round ball. Roll each ball in cinnamon sugar, then place back on the parchment paper. The dough balls will be quite close together, that's okay. Cover and chill 1 hour.
Preheat oven to 400°F.
Line a half sheet pan with parchment or a silicone mat. Right before baking, roll each dough ball in the cinnamon sugar mixture again, then arrange on the sheet pan at least 3 inches apart. I can usually fit 6, maybe 8 cookies per pan. Don't crowd them.
Bake 8-9 minutes. They should look slightly underdone in the middle. Remove from the oven and immediately use a round cutter or upside down glass jar to scoot them into shape (scooting is optional!). Let cool on the sheet pan 5 minutes before transferring to a cooling rack to cool completely.