Preheat oven to 350°F.
In a small microwave-safe bowl, melt unsalted butter (1 stick, ½ cup) for 30-45 seconds until fully melted (no chunks).
Add in light brown sugar (½ cup) and granulated sugar (¼ cup) and use a spatula to stir until combined (* do not use a mixer).
Add egg (1 large) and vanilla extract (2 teaspoons), then mix.
Add baking soda (½ teaspoon), cinnamon (½ teaspoon), and salt (½ teaspoon), then mix until combined.
Add all-purpose flour (1 ½ cups) and mix until all the flour disappears into the dough.
Drop chunks of dough into a greased and parchment-lined 9x13" pan, then use a spatula or your hands (sprayed with nonstick cooking spray) to smooth it out.
Mix the topping by combining the granulated sugar (3 tablespoons) and cinnamon (¾ teaspoons) in a small bowl.
Sprinkle on top of the cookie cake until fully covered, then shake off any excess.
Bake at 350 degrees for 11-12 minutes - do NOT overbake or your cookies will not be soft.
Remove from oven and place entire pan on a cooling rack. Allow the cookie cake to cool completely before removing and cutting.
Use a gingerbread cookie cutter to cut into shapes.
To Make Frosting: Beat the softened unsalted butter (¼ cup, i.e. ½ stick) on medium-high speed for 2 minutes until smooth.
Turn the mixer to low speed then add the powdered sugar (¼ cup at a time, 1¼ cups total).
Add vanilla extract (1 teaspoons), pinch of salt, and cinnamon (⅛ teaspoon) turn mixer to medium speed.
One tablespoon at a time, add milk (1-2 tablespoons). Beat on high for 2-3 minutes until creamy and the frosting is at a good consistency to pipe.
Decorate and enjoy! This frosting will firm up so that you can gently stack them on your cookie tray.
