Preheat oven to 350 degrees F.
In bowl, lightly beat butter and sugars. Add egg, vanilla and milk and mix until smooth. In another bowl, whisk together flour, baking soda and baking powder, and then mix into wet ingredients. Mix in cornflakes and coconut. Roll batter into 2-inch round balls and place, leaving a 2-3 inch space between cookies, on a non-stick, parchment paper-lined, or greased cookie sheet. Gently press down cookies and then bake until light golden in colour, about 10-12 minutes.