Dissolve yeast in warm water. Set aside until foamy.
In a bowl, cream shortening with sugar. Beat in eggs. Add squash and mix until blended. Add warm milk and yeast mixture. Slowly add flour and salt. Continue to mix until dough pulls away from side of bowl. Add flour as needed to make a soft dough, being careful not to add too much. Let dough rise, covered, until doubled in size. Punch down, cover, then let rise again until doubled.
Preheat oven to 375°F. Grease four 9-inch cake pans.
Divide dough into four equal pieces, then divide each quarter into 12 pieces. Shape each piece into a ball.
Place balls in single layer, touching, in prepared pans. Cover and let rise until doubled. Bake for 20 minutes, or until lightly browned. Remove from pans and set aside to cool.