NOTE: If you cannot find cake yeast, you can use active dry yeast. About 3 packets of active dry yeast (6 3/4 tsp) is equal to one 2 oz yeast cake.
In a large bowl, combine water, salt, sugar, egg, and crumbled yeast. Mix thoroughly. Add a little flour, about 1-2 cups, to make a paste. Then add cooled shortening and beat vigorously. (This dough can be made in a stand mixer with a dough hook attachment.)
Slowly add remaining flour until a soft dough forms and begins to leave the side of the bowl as it's mixed. Place dough on a lightly floured surface and knead until smooth and elastic, about 10 minutes.
Place dough in a greased bowl and turn gentle to coat. Cover with a damp cloth or a greased piece of plastic wrap, and let rise in a warm place for about 3 hours, until dough has doubled in size.
Once dough has risen, gently remove from bowl and pinch off 18 pieces of dough and shape into 3-inch balls. Place on greased baking sheets, about 3 inches apart. Flatten tops of balls, loosely cover with greased plastic wrap, and let rise a second time for about 2-3 hours.
Preheat oven to 375 degrees. Bake buns in a preheated oven for 15-20 minutes, until tops are golden brown. Remove buns from baking sheets and cool on a wire rack. Brush tops with melted butter if desired. Makes 18 large sandwich buns. Enjoy!