Mix the dry ingredients. In a medium bowl, combine the flour, baking soda, cinnamon and salt. Set aside.
Mix the wet ingredients. In the bowl of a standing mixer, beat the butter on medium speed until pale and fluffy, about 2 minutes. Add the brown and granulated sugar and beat on medium speed until combined and fluffy. Reduced the speed to medium-low and combine the egg and vanilla with the batter.
Make the batter. Add the dry ingredients to the bowl and beat to combine, scraping down the bowl if needed.
Roll the cookies. In a small bowl combine the sugar and spices. Scoop about 2 tablespoons of dough, roll gently into a ball, and roll through the sugar and spice mixture. Place on a parchment-lined baking sheet. Chill for 1 to 3 hours up to overnight.
Make the frosting. While the dough chills, make the frosting. In the bowl of a mixer, beat the butter on medium speed until pale and fluffy, about 90 seconds. Add the confectioner’s sugar and slowly increase the speed to medium, beating until incorporated. For a fluffier frosting, add heavy cream and mix on medium speed until incorporated.
Bake. Preheat the oven to 350°F. Bake the cookies for 12 to 14 minutes. Let cool for 5 minutes on the sheet tray and then transfer to a wire rack to cool.
Frost. Once the cookies are completely cool, spread a layer of maple frosting over each cookie. Optional: Sprinkle each cookie with freshly grated nutmeg.