For filling, in medium saucepan combine chocolate and milk. Stir over low heat just until chocolate is melted and smooth; remove from heat. Stir in jam. Fold in coconut. Cover; set aside. Preheat oven to 350F. Grease thirty-six 1-3/4-inch muffin cups (recipe works best in metal pans); set aside.
In a large mixing bowl beat butter with electric mixer for 30 seconds. Beat in sugar, egg, and vanilla until well combined. Add flour, cocoa powder, baking powder, baking soda, and salt. Beat on medium speed just until combined. Divide dough in 36 equal pieces; shape in 1-inch balls. Evenly press a ball of dough on bottom and up sides of each muffin cup. Divide filling among cups.
Bake for 10 to 12 minutes or until crust is set and dry. Cool in muffin cups on wire rack for 15 minutes. Carefully remove tartlets; cool completely on rack. Sprinkle with sifted powdered sugar. Makes 36 tartlets.