Dissolve yeast and 1 teaspoon sugar in warm water in a large bowl, stirring well; let stand 5 minutes or until bubbly. Add remaining sugar, shortening, baking powder, salt, and 2 cups flour; beat at low speed of electric mixer until smooth. Stir in enough remaining flour to make a soft dough.
Place dough in a greased bowl, turning to grease top. Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in bulk.
Punch dough down; turn out onto a lightly floured surface, and let rest 5 minutes. Knead 4 to 5 times. Roll dough to 1/4-inch thickness; cut into 3-inch squares. Cut each square in half to form a triangle.
Gently drop dough triangles into deep hot oil (375°); fry only a few at a time, turning once. Cook until sopaipillas are golden brown. Drain on paper towels. Serve hot with honey.