In a medium mixing bowl, beat butter on medium-high speed 30 seconds.
Add sugar, cinnamon and nutmeg and beat until combined.
Beat in milk and rum extract.
Add flour slowly and mix until combined.
{Refrigerate dough if necessary before continuing.}
Roll dough into 1 inch balls and place on cookie sheet lined with wax paper.
Melt white chocolate; dip cookie dough balls into chocolate and sprinkle with toasted coconut.
Cool at room temperature or refrigerator until hardened.