Place egg whites in a large mixing bowl; let stand at room temperature for 30 minutes. Add vanilla; beat on medium speed until soft peaks form. Gradually beat in sugar, about 2 tablespoons at a time, on high until stiff glossy peaks form and sugar is dissolved. Gradually fold in coconut and nuts, about 1/2 cup at a time.
Drop by rounded tablespoonfuls 2 in. apart onto parchment-lined baking sheets. Bake at 275 degrees F for 25 minutes or until firm to the touch. Remove to wire racks to cool completely.
In a microwave safe bowl, melt chocolate; stir until smooth. Dip the bottom of each cookie in chocolate. Place on waxed paper-lined baking sheets. Refrigerate for 1 hour or until chocolate is set. Store in an airtight container.