Follow the steps in order for the best result.
In a large mixing bowl, thoroughly combine 2 cups of flour and the dry yeast.
In a saucepan, gently heat the milk, butter (or shortening), sugar, and salt until the mixture is warm. Stir continuously until the butter or shortening is completely melted.
Pour the warm milk mixture into the bowl with the flour and yeast. Add the egg and cooked winter squash.
Using an electric mixer, beat the combined ingredients on low speed for 30 seconds. Increase the speed to high and beat for 3 minutes.
Gradually stir in the remaining flour until a soft dough forms.
Turn the dough out onto a lightly floured surface. Knead the dough until it becomes smooth and elastic.
Place the kneaded dough in a lightly oiled bowl, turning to coat all sides. Allow the dough to rise in a warm place until it has doubled in size, approximately 1 1/4 hours. For a slower rise, you can refrigerate the dough overnight.
Once the dough has doubled, punch it down to release the air. Let it rest for 10 minutes.
Roll out the dough and shape it into individual rolls, or use a biscuit cutter to create uniform shapes.
Place the shaped rolls on a baking sheet and let them rise again until noticeably puffy.
Preheat your oven to 400 degrees F (200 degrees C). Bake the rolls for 10 to 12 minutes, or until they are golden brown.
Remove the baked rolls from the oven and immediately brush them with melted butter.