In a large mixing bowl, whisk together the flour, cream of tartar, baking soda, and salt; set aside.

In the bowl of a stand mixer fitted with a paddle attachment, beat the butter until smooth, about 1 to 2 minutes. Add both sugars and continue beating on medium speed until smooth and creamy.

Scrape down the sides of the bowl, add the eggs, one at a time, beating until just combined. Add the milk and vanilla and beat on medium-high speed. Dump in the flour mixture and beat on low for about 1 minute.

Dollop half of the dough into a greased 10-inch cast iron skillet. Wrap the other half in plastic wrap. Place both in the freezer for 15-20 minutes so that dough is less sticky and easier to work with. In a small dish, combine the 1/4 cup of sugar and 2 teaspoons of cinnamon with a fork or spoon.

Preheat oven to 350ºF. Once chilled, press the dollops of dough into an even layer in the bottom of the skillet. Sprinkle with half of the cinnamon-sugar.

Spoon dollops of the cookie butter evenly over the dough. Take chunks of the remaining dough, flatten slightly*, and layer them side by side on top of the cookie butter. Try to cover as much of the cookie butter as possible. Sprinkle with the last half of the cinnamon-sugar.

Bake for 27-30 minutes, or until edges are lightly golden. Allow to cool for at least 20-30 minutes. Serve with a scoop of ice cream, if desired.