Heat oven to 375°F. In shallow baking pan, spread coconut evenly and toast, stirring twice, until lightly golden, 4 to 6 minutes. Cool coconut.
In small bowl, sift together flour, baking soda, and salt. In large bowl, with electric mixer on medium, beat butter and sugars until light and fluffy. Beat in egg and vanilla; stir in flour and coconut until blended.
Arrange level teaspoonfuls of dough about 2 inches apart on ungreased baking sheets, and bake for 8 to 10 minutes, or until golden. Cool cookies on sheets 1 minute. Transfer to wire racks; cool completely. Repeat with remaining dough.
Sandwich with melted chocolate.