Beat the butter, sugar, and vanilla with an electric mixer until light and creamy. Add the egg and beat well. Add the plain and self-rising flours and coconut and mix well. Add the chocolate.
With a large oxo cookie/ice cream scoop parcel out the dough and flatten slightly with a bottom of a glass. Place on a baking tray lined with non-stick baking paper or Silpat silicone liner. Leave 1" space between each cookie to allow for cookies to spread. , leaving room to spread. Repeat with remaining mixture. Bake for 10 to 14 minutes or until lightly golden. Allow cooling on trays.
Donna's notes: To check if the cookies are done, look at the bottom, not the top. If you wait until the top looks right you risk overcooking them. To check, lift a cookie with a spatula so you can see underneath. The bottom should be deep golden. Cool on trays as the cookies will continue to cook after you've removed them from the oven.