1In a large bowl, dissolve yeast in warm water. Add 1 teaspoon sugar; let stand for 5 minutes. Add the milk, shortening, salt, egg, remaining sugar and 2 cups flour; beat until smooth. Stir in enough remaining flour to form a soft dough (dough will be sticky). Do not knead. Cover and refrigerate for 8 hours or overnight.
For filling, combine sugar and tapioca in a small saucepan; add strawberries. Let stand for 5 minutes. Bring to a boil; cook and stir for 2 minutes or until thickened. Stir in the lemon juice. Cool.
Punch down dough; divide in half. On a lightly floured surface, roll each portion to 1/4-in. thickness. Cut into 2-in. squares. Spoon about 1/2 teaspoon of filling into the center of each square. Bring two opposite corners together over center of filling; pinch to seal. Place 2 in. apart on greased baking sheets. Cover and let rest for 15 minutes.
Bake at 425° for 8-10 minutes or until golden brown. Remove to wire racks. Brush with melted butter; cool. For icing, in a small bowl, cream shortening and butter until light and fluffy. Gradually beat in the confectioners' sugar, vanilla and enough milk to achieve desired consistency. Drizzle over pastries. Yield: 2-1/2 dozen.