Whisk together flour, cocoa powder, malted milk, cornstarch, baking soda and salt. Set aside.
In a stand mixer fitted with paddle attachment, cream butter and sugars. Add egg and beat well to combine, then add vanilla. Slowly stir in in dry ingredients. Dough will be stiff. Chill for at least 1 hour.
Preheat oven to 350°F. Line baking sheet with parchment. Roll dough into 1-inch balls and space at least 2 inches apart. Bake for 8 minutes. Remove from oven and let rest on pan for 2 minutes before removing to a wire rack to cool completely before frosting.
For the frosting:
Cream butter and powdered sugar until crumbly.
In a separate bowl, combine malt powder, heavy cream and vanilla until smooth. Slowly stir into butter mixture. Increase speed and whip until light and fluffy.