In a small saucepan, combine cut-up chocolate and shortening; heat and stir over low heat until melted. Remove from heat. Evenly brush inside of each phyllo shell with melted chocolate mixture. Chill phyllo shells about 20 minutes or until chocolate is set.
Meanwhile, in a small bowl, stir together cream cheese, sour cream, and powdered sugar until smooth. Stir in apricot brandy or nectar. Spoon 1 rounded teaspoon of the cream cheese mixture into each shell. Cover loosely; chill for 2 to 4 hours or until completely chilled.
Remove from refrigerator and allow to stand at room temperature about 30 minutes before serving. If desired, place a strawberry quarter on top of each tassie. Makes 15 tassies.