Preheat the oven to 350F. Line 2 cookie sheets with parchment paper or silicone baking mats.

In a mixing bowl, whisk together flour, cornstarch, baking soda, and salt. Set aside.

In a large mixing bowl, cream the butter, brown sugar, and ⅓ cup granulated sugar with an electric mixer until flurry. Mix in the egg and vanilla extract. 

Add the dry ingredients and mix just until blended. Cover bowl with plastic wrap and chill 15 minutes.

Prepare Cinnamon Sugar Coating: Place ¼ cup granulated sugar and cinnamon in a small bowl and stir to combine. 

Scoop balls of cookie dough (each about 1 tablespoon) and roll them between your palms. Roll the balls in the cinnamon sugar and place 2 inches apart on your cookie sheet. These do spread, so make sure to space them accordingly. 

Bake for 10 to 13 minutes, or until they are lightly golden and have lost their glossy sheen. Cool completely before frosting.

To make the frosting: beset the butter in a large bowl with an electric mixer until smooth. Slowly mix in they powdered sugar until crumbly; then mix in the cinnamon, vanilla, and slat. Add 1 tablespoon milk and mix until smooth, adding more milk as desired for spreadable consistency. 

You can frost the cookies any way you like, but to decorate them as shown, place the frosting in a bag fitted with an open star tip (such as Wilton No. 199). Pipe the frosting in a round squirm motion all over the top of the cookie.