In the bowl of an electric mixer fitted with the dough hook attachment, stir the yeast, milk, sugar, butter, pumpkin, one egg, cheddar, and salt until well combined. Gradually add the flour and knead on medium-low speed until the dough pulls away from the sides of the bowl. Turn off the mixer and let the dough rest for 3 to 5 minutes. Continue to knead the dough on medium-low speed for another 5 minutes, or until the dough is soft and smooth. If it seems too sticky, add more flour, 1 tablespoon at a time.
Transfer the dough to a large greased bowl. Cover the bowl with plastic wrap and let the dough rise until doubled in size, about 45 minutes to 1 hour.
Punch the dough down and turn it out onto a lightly floured work surface. Divide the dough into 15 equal pieces and shape into balls. Use the palm of your hand to flatten each ball slightly. With a small knife, cut 8 slices around each ball, being careful not to slice all the way into the center, to make the pumpkin shape. Cover and let rise until doubled in size, about 45 minutes to 1 hour.
Meanwhile, preheat the oven to 350°F. Using the wooden end of a small utensil or your finger to poke an indentation in the center of each roll to create a space for the “stem.” In a small bowl beat the remaining egg with 2 teaspoons of water and brush all over the rolls. Bake the rolls for 15 to 20 minutes, or until golden brown. Place a sliced pecan piece into the indentation of each roll.