Melt butter in 10-inch skillet; stir in brown sugar and dates. Remove from heat. Stir in egg; return to heat. Cook over medium heat, stirring constantly, until mixture comes to a full boil (4 to 6 minutes). Boil, stirring constantly, 1 minute.
Remove from heat; stir in 1 cup coconut and all remaining ingredients until moistened. Let stand 10 minutes.
Shape rounded teaspoonfuls into 1-inch balls; roll in remaining coconut.