Place pumpkin in a small saucepan. Heat over medium heat until pumpkin registers 100F degrees. Remove from heat and set aside.
In a large bowl, dissolve yeast in warm water. Let sit 5 minutes, then stir in oil, honey, eggs, salt, and warm pumpkin until smooth. Stir in 2-1/2 cups flour until mixture forms a soft dough. (dough should be slightly sticky)
Turn dough onto a floured surface. Knead dough until smooth and elastic, about 5 minutes. Place dough in a greased bowl, turning once to grease top. Cover bowl with a kitchen towel, and let rise in a warm place until dough is doubled, about 1-1/2 hours.
Punch dough down, and shape dough into 12 balls. Place on two parchment paper-lined baking sheets. Cover rolls with a kitchen towel and let rise in a warm place until doubled, about 30 minutes.
Bake rolls at 375F 20-22 minutes until golden brown. Brush each roll with softened butter and transfer to a cooling rack to cool completely.
Store rolls in an airtight container at room temperature up to 2 days.