Preheat oven to 350°F With a stand or hand mixer, cream together softened margarine, flavours, and sugar until light in colour, about 2-3 minutes.
Turn mixer to low and slowly add flour, cornstarch, and baking powder. Mix until just combined and turn onto counter to finish dough by lightly kneading by hand.
Pinch off small pieces of dough and roll into 1-inch balls. Place balls on parchment-lined baking trays and flatten slightly with your thumb. Bake for 12 to 14 minutes, checking halfway. Rotate pans if needed.
While cookies are baking, combine all icing ingredients except plant milk in a separate bowl and beat until smooth. Add plant milk one tablespoon at a time to make a creamy mixture. Icing should hold its shape but still be soft enough to spread without breaking the cookie.
Personalize your cookie! Add food colouring to icing if desired. Ice cooled cookies (you can use a knife or a piping bag) and top with a pinch of nutmeg or a few sprinkles.