Dissolve yeast in warm water; let stand 5 minutes.
Combine flour, salt, baking powder, and sugar; cut in shortening. Make a well in center of mixture. Add yeast mixture and milk, mixing well. (Dough will be sticky).
Turn dough out onto a lightly floured surface, and knead 15 to 20 times. Roll dough to 1/4-inch thickness; cut into 3-inch squares.
Heat 1/2 inch of oil in a large skillet to about 370°. Gently place dough squares in oil, a few at a time, lightly pressing down with a spatula until dough starts to bubble and puff. Turn and cook on other side until barely golden in color; drain. Sprinkle with powdered sugar or serve with honey, if desired.
Note: When frying sopaipillas, leave a few in skillet while adding additional ones. The ones left in the skillet will absorb the heat of the oil and keep it from overheating.