Preheat the oven to 350 and grease a 9x13 baking pan.
In the bowl of an electric mixer, cream together butter and sugar for a couple of minutes on medium-high speed.
Add egg and vanilla and beat until mixed. Scrape sides and bottom of the bowl.
Beat in maple syrup.
Turn off and sift in the flour, baking soda, and salt. Mix ingredients on low speed until just combined. Scrape sides and bottom of the bowl and mix a couple more times.
Spread cookie batter in the baking dish, evenly.
Bake for 18-20 minutes. Take out and let it cool completely before frosting.
Frosting:
Beat butter on medium-high speed for a couple of minutes.
Turn off the mixer and sift in powder sugar and cinnamon. Start mixing on low until sugar is incorporated. Beat on high for a couple more minutes.
Drizzle in maple syrup and vanilla extract while mixing and beat for about 30 more seconds. Scrape sides and bottom of the bowl and beat for a few more seconds.
Once cookie is completely cooled, evenly spread the frosting on top.