Line a 9x13 inch metal pan with parchment paper and butter the sides/spray it with cooking spray. Set aside.
Combine 8 tablespoons butter with ¾ cup sugar and beat in a stand mixer or with a hand mixer until light and fluffy. Add milk and egg and beat until combined, then an extra 10 seconds more. Add 1 ½ cups flour, cream of tartar, baking soda, and salt, and beat on low until just combined.
Scrape batter into the pan and spread evenly to the edges using a knife or a spatula. (Dolloping all over the bottom of the pan works well, but I still find I need to use clean, wet fingertips to push the batter into the corners and edges since the parchment moves around.) Set pan aside.
Gooey Layer
Whisk together corn syrup, milk, and vanilla, and set aside. In the bowl of an electric mixer, beat 12 tablespoons butter, 1 cup and 2 tablespoons sugar, and ¼ teaspoon salt until light and fluffy. Beat in the egg until combined, and then beat an extra 10 seconds more. Add ⅓ of the remaining flour, then ½ of the milk mixture. Add another ⅓ flour, then the remaining milk, and then the rest of the flour, mixing only until just combined. Pour and spread batter over the cookie base and spread to the edges of the pan as necessary. (This is a thinner batter than the base, so this is much easier.)
Cinnamon Sugar Topping
Combine the 2 tablespoons sugar with the cinnamon, then sprinkle evenly on top of the batter.
Bake at 350F for 25-30 minutes (27 is perfect in my oven). The center will still be liquidy and jiggle; this will make goo. Cool completely, then cut into several little squares.