Cream sugar and butter with mixer; add egg and beat until combined.
Add dry ingredients to a sifter. Alternate adding milk and dry ingredients to the butter mixture while mixing. Then add vanilla and stir.
Chill for 30 minutes before rolling out. Roll out the dough on a floured surface (adding more flour to the dough if it's too sticky) until it's ~1/8-inch thick. Cut into ~2-inch x 2-inch squares and bake at 375 degrees for 10-11 minutes, being careful not to over-bake.
To make the frosting, cream softened butter with 1 cup of the powdered sugar and then slowly add in the rest.
Add maple extract (I used greater end of range // 3 tsp as original recipe is written) and milk, and stir. The consistency you’re looking for is thick and spreadable; not runny.
Frost cookies, sprinkle with cinnamon and enjoy! Store in an air-tight container at room temperature to keep fresh for at least 3 days.
*Questions about substitutions, equipment, or troubleshooting? Check out our Recipe FAQ page. *Nutrition information is a rough estimate.