Preheat oven to 350 degrees. Grease a cookie sheet and set aside.
In a large bowl, cream together the butter and sugar.
Add in the egg and vanilla extract.
Continue to mix until light and fluffy.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Add half of the dry mixture to the wet mixture. Mix.
Add 1 tbsp of milk and continue to mix.
Mix in the remaining dry mixture.
Finally, mix in the last of the milk.
Add in the green food color and continue to mix until your batter is no longer crumbly and completely green.
Take golf-ball sized balls of dough and roll them in the palms of your hands until smooth.
Place the green sugar in a small bowl.
Roll the Grinch Christmas cookie dough balls into the green sugar and arrange them on a cookie sheet, 1 inch apart.
Bake in the oven for 12-13 minutes, until they are just lightly brown around the edges.
Remove from the oven and let cool 2 minutes.
Working quickly, press a candy cane kiss cookie into the center of each Grinch sugar cookie.
Let the cookies cool for 10 minutes and then carefully transfer them to a cooling rack to finish cooling.
Store in an air-tight container.