Preheat the oven to 400 degrees F (200 degrees C).
In a small saucepan, cover squash cubes with water. Bring to a boil and cook until tender, about 15 minutes. Drain; cool and mash.
In a small bowl, dissolve yeast in warm water.
In a large bowl, combine 5 cups flour, sugar, and salt. Stir in yeast mixture, shortening, squash and milk; mix well.
Stir in remaining flour, ½ cup at a time, beating well after each addition.
When dough has pulled together, turn out onto a lightly floured surface and knead until smooth and supple, about 8 minutes.
Lightly oil a large bowl, place dough in the bowl and turn to coat with oil.
Cover with a damp cloth and let rise in a warm place until doubled in volume, about 1 hour.
Divide dough into twelve equal pieces and form into rounds.
Place the rounds in a lightly greased 13x9-inch baking pan.
Cover with a damp cloth and let rise until doubled in volume, about 30 minutes.
Meanwhile, preheat the oven to 400 degrees F (200 degrees C).
Bake rolls in the preheated oven for 10 to 15 minutes or until golden brown.
