In a large bowl or bowl of a stand mixer, combine 1 ¾ cups flour, sugar, salt, cinnamon, ginger, cloves, nutmeg and yeast. Add pumpkin, warm water, butter and eggs. Stir, adding just enough of remaining 1 ½ cups flour until a dough forms that pulls away from sides of bowl.
On a lightly floured surface, knead dough by hand 10 minutes until smooth, soft, elastic and only slightly sticky; OR, knead dough with dough hook attachment in stand mixer on medium speed 5 minutes until smooth, soft, elastic and only slightly sticky. Shape dough into a ball, then place in a large lightly greased bowl; turn to coat. Cover bowl with plastic wrap and let rise in a warm place 1 hour until doubled.
Heat oven to 375 degrees. Line a baking sheet with parchment paper. Punch down risen dough, then divide into 12 equal pieces. Roll each piece into a ball, then place on prepared baking sheet spaced at least 2 inches apart. Cover with a tea towel or lightly greased plastic wrap and let rise 30 minutes until doubled.
Just before baking, use scissors or a sharp serrated knife to score tops of rolls about 1/4-inch deep. Brush tops and sides of rolls with egg wash. Bake 20 to 25 minutes until golden brown.