Preheat the oven to 350 degrees. Line a 9x13 rimmed cookie baking sheet with parchment paper.
Heat 12 tablespoons of butter in a cooking pan, over medium-high heat, until melted. Continue cooking, slowly and constantly stirring, until butter is darkened to golden brown and has a nutty aroma, about 3 minutes.
Transfer browned butter into a large, heatproof mixing bowl.
Whisk in both sugars and vanilla extract until fully incorporated.
Whisk in eggs, one at a time, until mixture is smooth with no lumps remaining, about 30 seconds. Let mixture stand a couple of minutes, then vigorously whisk for 30 seconds. Repeat process of resting and whisking a couple more times until mixture is thickened, smooth, and shiny.
Using a rubber spatula, stir in flour, cinnamon, and baking soda until just combined, about 1 minute.
Transfer the batter into the prepared baking sheet and spread it all over. Make sure the batter is as even as possible all over, around the edges and the center.
Bake for about 15-17 minutes. Take out and let it cool completely before attempting to frost.
Frosting:
Beat butter on medium-high speed for a couple of minutes. Switch to a whisk attachment.
Sift in powder sugar and cinnamon. Start mixing on low until sugar is incorporated. Pour in heavy whipping cream, mix it in and scrape sides and bottom of the bowl. Turn the speed back to medium-high. Beat for a few more minutes.
Spread frosting all over the cooled cookie base. Sprinkle some cinnamon on top and cut.