Preheat 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 the yeast mixture, shortening, squash and milk. Mix well. Stir in the remaining flour, 1/2 cup at a time, beating well after each addition. When the dough has pulled together, turn it out onto a lightly floured surface and knead until smooth and supple, about 8 minutes. Lightly oil a large bowl, place the 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 the 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.
Bake at 400 degrees F (200 degrees C) for 10 to 15 minutes or until golden brown.